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ALL    RIGHTS     RESERVED.        PUBLISHED     JULY     19iJ9 



In  presenting  this  book  to  the  public  I  am  spared  an  embar- 
rassment that  many  writers  encounter ;  I  do  not  need  to  give  an 
apology  for  the  topic  with  which  it  deals.  Alfred  Weber's  treat- 
ise is  a  pioneering  venture.  He  attempts  to  master  by  theoreti- 
cal analysis  a  complete  wilderness  of  facts  which  has  grown  up 
around  us  during  the  last  two  centuries  concerning  the  location 
of  our  modern  manufacturing  industries.  To  be  sure,  others 
have  ventured  upon  the  task  of  describing  and  classifying  the 
phenomena  of  geographical  distribution;  but,  as  Weber  points 
out,  previous  writers  did  not  get  beyond  a  mere  enumeration  of 
various  factors  which  played  a  part  in  determining  the  location 
of  industries. 

While  I  am  quite  impressed  with  the  importance  of  Weber's 
work  itself,  if  clearly  understood,  it  is  precisely  this  task  of  mak- 
ing it  understood  about  which  I  feel  very  apologetic.  In  spite  of 
the  help  and  advice  which  Professors  Leon  C.  Marshall  and 
Frank  W.  Taussig,  as  well  as  Drs.  E.  H.  Chamberlin,  William 
Y.  Elliot,  Edward  Mason,  Talcott  Parsons,  and  Andreas  Pre- 
döhl  have  so  generously  afforded  me,  I  do  not  feel  confident 
that  I  have  succeeded  in  conquering  the  difficulties  which  con- 
front the  translator  of  such  a  highly  abstract  treatise.  Had  not 
Professor  Marshall  and  Dr.  Mason  read  the  entire  manuscript 
through  and  made  numerous  suggestions  for  its  improvement,  I 
fear  I  should  not  have  found  the  courage  to  let  it  see  the  light  of 

It  will  be  conceded  by  those  who  have  embarked  on  the 
hazardous  adventure  of  translating  abstract  thought  from  one 
language  into  another  that  nothing  is  more  perplexing.  It  is  in 
such  thought  that  the  Sprachgeist  develops  its  subtlest  distinc- 
tions, successfully  defying  either  translating,  transcribing,  or 


viii  PREFACE 

paraphrasing.  For  this  reason  the  paging  of  the  German  edition 
of  Weber's  book  has  been  inserted  as  marginal  notes  through- 
out. These  notes  are  usually  inserted  at  the  end  of  a  sentence, 
even  though  that  sentence  overlaps  the  page  in  the  original. 
The  interested  reader  will  consult  the  German  text  wherever 
the  English  translation  becomes  too  obscure.  Had  space  per- 
mitted, I  should  have  included  the  German  text  itself.  But, 
after  all,  the  greatest  usefulness  of  such  a  translation  is  the  as- 
sistance it  may  give  to  the  student  who  knows  the  original  lan- 
guage, but  does  not  know  it  sufficiently  well  to  enable  him  to 
make  the  entire  translation  himself. 

Comparison  with  the  German  text  will  show  that  Weber's 
preface  to  the  first  and  second  (unaltered)  edition,  as  well  as  his 
two  notes  (Exkurse)  have  been  omitted.  We  should  have  been 
glad  to  include  Weber's  contribution  to  the  Grundriss  der  So- 
zialökonomik^  could  it  have  been  arranged.  I  can  only  refer  to 
this  treatise  all  readers  who  are  particularly  interested  in  those 
aspects  of  location  which  Weber  touches  upon  in  his  introduc- 
tion and  in  his  last  chapter  as  well  as  in  the  paragraphs  through- 
out the  book  on  tendencies  of  development.  It  seemed  impor- 
tant to  include  the  mathematical  appendix  by  Georg  Pick.  I  sin- 
cerely hope  that  the  indulgent  reader  will  not  feel  as  did  that  stu- 
dent who  wrote  on  top  of  Alfred  Marshall's  mathematical  ap- 
pendix to  his  Principles:  ''A  bad  case  of  appendicitis — cut  it 
out."  In  translating  this  mathematical  appendix  I  have  had  the 
valuable  advice  of  Mr.  Paul  S.  Bauer. 

This  study  would  probably  not  have  been  possible  without 
the  constant  encouragement  of  Professor  Leon  C.  Marshall.  I 
wish  to  thank  him  and  all  others  who  have  helped  me. 

C.  J.  F. 

^"Industrielle  Standortslehre  (Reine  und  kapitalistische  Theorie  des  Stand- 
orts)," in  Grundriss,  Abteilung  VI,  B,  particularly  the  second  part  dealing  with 
capitalistic  theory. 



Editor's  Introduction:  The  Theory  of  Location  in  Relation  to 

THE  Theory  of  Land  Rent xiii 

1.  In  John  Stuart  Mill xiii 

2.  In  Alfred  Marshall  .      .      .      .    " xv 

3.  In  J.  H.  von  Thiinen xix 

4.  In  Alfred  Weber xxii 

5.  Significance  for  a  Theory  of  Monopoly,  Transportation  Rates, 

and  International  Trade .  xxix 

Author's  Introduction i 

1.  Importance  of  an  Economic  Theory  of  Location      ....  i 

2.  Limitation  to  a  Theory  of  the  Location  of  Manufacturing 
Industry;  Reasons  Therefor 4 

3.  Method  Employed 8 

4.  Limitations  of  the  Results 12 

Chapter  I.  LocATioNAL  Factors  and  LocATiONAL  Dynamics  17 

I.  The  Terms  "Locational  Factor"  and  "Locational  Unit"       .  17 

IL  Classification  of  Locational  Factors 20 

a)  General  and  Special 20 

b)  Regional  and  Agglomerative 20 

c)  Natural  and  Technical,  Social  and  Cultural     ....  21 

III.  Ascertaining  the  General  Factors  of  Location       ....  23 

a)  Ascertaining  the  Individual  Regional  Factors       ...  23 

b)  Costs  of  Transportation  and  Labor  Costs  Are  the  Only 
Regional  Factors 29 

IV.  Theory  of  the  Locational  Factors 34 

Chapter  II.  Simplifying  Assumptions 37 

I.  The  Assumption  of  a  Separate  Basis  of  Material  Supply,  Con- 
sumption, and  Labor .  37 

II.  The  Consideration  of  the  "Forces  of  Nature" 39 

Chapter  I^I.  Transport  Orientation  (Transportorientierung) 

Section  I.  Analysis  of  Transportation  Costs 41 

I.  Weight  and  Distance  the  Only  Elements  of  Cost  in  Our 

Theoretical  Analysis 41 




2.  The  Type  of  the  Transportation  Sj^stem  and  the  Extent  of 

Its  Use 43 

3.  The  Nature  of  the  Locality  and  Its  Kinds  of  Roads  .      .  45 

4.  The  Nature  of  the  Goods 45 

5.  Relation  to  Reality 46 

Section  IL  The  Laws  of  Transport  Orientation 48 

1.  The  Locational   Figures   and   the   Kinds   of  Industrial 
Materials 48 

2.  Mathematical  Solution 53 

3.  Material    Index,    Locational    Weight,    and    Theoretical 
Conclusion 59 

4.  Cases 61 

5.  The  Orientation  of  an  Entire  Industry 67 

a)  The  Creation  of  the  Individual  Figures       ....  67 

b)  Co-operation  of  the  Individual  Figures        ....  70 

6.  The  Factors  of  Transport  Orientation 72 

7.  Tendencies  of  Development 73 

Section  III.  Approximations  to  Reality 76 

1.  The  Existing  System  of  Transportation  Rates       ...  76 
A.  Deviations    from    the    Pure    Calculation    of    Rates 

According  to  Mileage 77 

A.  Deviation  from  the  Pure  Calculation  of  Rates  Accord- 
ing to  Weight 78 

2.  The  Real  Nature  of  the  Transportation  System    ...  81 

A.  A  Divided  System  of  Transportation 81 

B.  Different  Kinds  of  Transportation  Systems  Working 
Together 82 

a)  The  Effect  of  the  Waterways 84 

b)  The  Effect  of  the  Net  of  Highways 86 

3.  Further  Applications  of  the  Theory  to  Reality      ...  88 

A.  The  Price  Differences  of  Materials  and  Their  Effect  .  88 

B.  The  Use  of  Water  Power .      .  89 

a)  The  Use  of  Waterfalls 89 

b)  Transmissible  Water  Power 91 

Chapter  IV.  Labor  Orientation 95 

Section  L  The  Analysis  of  Labor  Costs 95 

1.  The  Geographical  Differences  in  Labor  Costs 95 

2.  Their  "Forms  of  Occurrence";  Differences  Accordini7  to 
Area 97 

3.  Simplifying  Assumptions 100 



Section  II.  The  Law  of  Labor  Orientation 102 

1.  Theoretical  Solution;  Isodapanes 102 

2.  The  Conditions  of  Labor  Orientation 105 

3.  The  Character  of  the  Industries  and  Labor  Orientation  107 

A.  Orientation  of  an  Individual  Plant:  Index  of  Labor 
Costs  and  Coefficient  of  Labor 107 

B.  Orientation  of  an   Entire   Industry:  Elimination  of 
Labor  Locations  and  Replacement  of  Deposits      .  112 

4.  The  Environmental  Conditions  of  the  Labor  Orientation  117 

5.  Tendencies  of  Development 120 

Chapter  V.  Agglomeration 124 

Section  I.  Analysis  of  Agglomerative  and  Deglomerative  Factors 

1.  Object  of  the  Analysis 124 

2.  Definitions:  Function    of    Economy    and    Function    of 
Agglomeration 126 

3.  Agglomerative  and  Deglomerative  Factors       .      .  127 

A.  Agglomerative  Factors 127 

a)  Development  of  the  Technical  Equipment  .  128 

b)  Development  of  the  Labor  Organization  129 

c)  Marketing  Factors 130 

d)  General  Overhead  Costs 130 

B.  Deglomerative  Factors 131 

Section  IL  The  Laws  of  Agglomeration 134 

A.  Agglomeration  within  Transport  Orientation 135 

1.  Agglomeration  with  Fixed  Index 135 

a)  When  Does  Agglomeration  Take   Place,   and  How 
Much? 135 

b)  Where  Will  Agglomeration  Take  Place?    ....  138 

c)  The  Size  of  the  Unit  of  Agglomeration 139 

d)  Modifications 141 

2.  Agglomeration  in  the  Case  of  an  Increasing  Index      .  143 

3.  The  Conditions  of  Agglomeration 147 

4.  The  Formula  of  Agglomeration 153 

B.  Agglomeration  and  Labor  Orientation 156 

Section  HI.  Reintroducing  the  Realities 162 

1.  Coefficient    of    (Value    Added    through)    Manufacture 
(Formkoeffizient) 162 

2.  The  Forms  of  Agglomeration  in  Reality 166 

3.  Tendencies  of  Development 168 



Chapter  VI.  The  Total  Orientation 173 

Section  I.  The  Organization  of  the  Stages  of  a  Given  Productive 

Process 174 

A.  The  Stages  of  Production  and  Transport  Orientation  174 

1.  When  Does  a  Split  Occur  in  the  Production?    .  174 

2.  Where  Will  the  Locations  of  the  Productive  Stages  Be 
When  Production  Is  Split? 178 

3.  A  More  Precise  Answer  to  the  Question:  When  Does  a 
Split  in  the  Production  Occur? 182 

4.  Complications  (Replacement  of  Material  Deposits)    .      .  183 

B.  The  Stages  of  Production  and  Labor  Orientation       .  184 

C.  The  Stages  of  Production  and  Agglomeration       ....  186 

D.  Reintroducing  the  Realities 187 

1.  General  Observations 187 

2.  Tendencies  of  Actual  Development 190 

Section   II.  The   Interaction   of    the    Independent    Productive 

Processes 196 

1.  The  Coupling  of  Independent. Productive  Processes   .  197 

2.  Connection  through  Materials 201 

3.  Market  Connection 206 

4.  The  Total  Orientation 209 

Chapter  VII.  Manufacturing  Industry  within  the  Economic 

System 211 

Introductory  Remark 211 

I.  Historical  Distribution  of  Locations 213 

IL  The  Strata  of  Locational  Distribution  and  Their  Interaction  214 

III.  The  Result  and  the  Remaining  Problem 221 

Mathematical  Appendix,  hy  Georg  Pick 226 

Introductory  Remark 227 

I.  The  Locus  of  the  Least  Costs  of  Transportation  .  227 

IL  Curves  of  Equal  Transportation  Cost        240 

HI.  Agglomeration 245 

Index 253 




"Knowledge  insufficient  for  prediction  may  be  most  valua- 
ble for  guidance,"  wrote  John  Stuart  Mill,  in  discussing  eco- 
nomic theory  in  general.^  This  statement  might  very  properly 
have  been  made  the  motto  of  Weber's  attempt  to  analyze  a 
much-neglected  problem  by  what  Mill  would  have  called  a  strict- 
ly deductive  method.  This  problem  is:  what  causes  an  indus- 
try^ to  change  its  location? 

The  change  of  industrial  location  is  among  the  most  gener- 
ally discussed  economic  problems  of  today.  In  the  nation-wide 
agitation  for  power  development  in  the  United  States,  for  ex- 
ample, the  argument  is  quite  generally  used  that  it  will  ''decen- 
tralize" industries.^  English  economic  theory,  however,  has  neg- 
lected a  strictly  theoretical  analysis  of  the  problem.  From 
Adam  Smith  to  Pigou  no  adequate  deductive  treatment  of  the 
causes  determining  economic  location  has  been  attempted,  in 
spite  of  the  fact  that  such  an  analysis  may  be  capable  of  aiding 
in  further  refining  the  theories  of  monopoly,  transportation  rates, 
and  international  trade. 

John  Stuart  MilP  touches  upon  the  problem  when  consid- 

"  Logic,  Book  6,  chap,  ix,  §2. 

^  "Industry"  is  used  here  and  throughout  in  the  sense  of  manufacturing  in- 
dustry, unless  stated  otherwise. 

*So  Secretary  Hoover.  Compare  his  address  at  the  First  International 
Power  Conference,  London,  1927,  Prosperity  Through  Power  Development. 
Compare  also  the  many  generalizations  which  are  made  in  order  to  explain  the 
movement  of  industries  to  the  South, 

"It  is,  of  course,  arbitrary  to  begin  with  Mill,  but  it  may  be  justified  on 
grounds  of  expediency,  since  he  more  or  less  systematized  and  correlated  the 
thought  of  those  before  him.    I,  for  one,  should  Hke  to  include  at  least  Adam 


ering  value.  In  enumerating  the  various  channels  through  which 
labor  cost  influences  the  cost  of  production  he,  like  previous 
writers,  includes  the  cost  of  transporting  materials  to  the  place 
of  production  and  the  cost  of  '^conveyance  of  products  to  the 
market."*^  But  he  does  not  consider  the  variability  of  this  factor 
as  affecting  the  place  of  production,  although  some  of  the  direct 
effects  of  purely  locational  factors  did  attract  his  attention.  "Al- 
most all  kinds  of  raw  material  extracted  from  the  interior  of 
the  earth — metals,  coals,  precious  stones,  etc.,  are  obtained  from 
mines  differing  considerably  in  fertility,  that  is,  yielding  very 
different  quantities  of  the  product  to  the  same  quantity  of  labor 
and  capital."  But  he  apparently  despaired  of  explaining  this 
phenomenon,  since  he  goes  on:  "Whatever  the  causes,  it  is  a  fact 
that  mines  of  different  degrees  of  richness  are  in  operation,  and 
since  the  value  of  the  produce  (the  costs)  must  be  proportional 
to  the  cost  of  production  at  the  worst  mine  (fertility  and  situa- 
tion taken  together),  it  is  more  than  proportional  to  that  of  the 
best."'  Here  "situation"  (which  corresponds  to  our  term  "loca- 
tion") emerges  for  a  moment  as  a  factor,  but  immediately  dis- 
appears again  behind  the  more  usual  consideration  of  "fertility." 
But  this  factor  of  "location,"  whose  determining  causes  seem  so 
elusive  to  Mill,  may  be  capable  of  rational  explanation  if  only 
we  carry  our  inquiry  one  step  farther  and  analyze  the  factors 
which  determine  what  is  and  what  is  not  a  "favorable"  location. 
We  shall  return  to  this  point  presently.  It  remains  to  call  atten- 
tion here  to  the  fact  that  the  passages  just  discussed  appear  in 

Smith  and  Ricardo,  because  of  their  relation  with  the  system  of  Von  Thiinen. 
But  the  pecuharities  of  their  theories  of  rent  would  require  too  much  time  to 
review  for  the  particular  problem  in  hand  (cf.  Schumpeter,  Epochen  der  Dog- 
men-und  Methodengeschichte,  pp.  87  ff.).  It  is  not  very  difficult,  moreover,  to 
apply  what  is  here  said  about  John  Stuart  Mill  to  the  earHer  thinkers. 

^Principles  (New  York,  1874,  from  the  sth  London  edition).  Book  III, 
chap,  iv,  §1.  In  succeeding  notations  Roman  numerals  refer  to  book,  Arabic  to 
section,  unless  otherwise  indicated. 

''Principles,  III,  chap,  v,  3.  The  itahcs  are  mine. 


connection  with  Mill's  analysis  of  rent  in  its  relation  to  value.  It 
may  not  be  amiss  to  quote  another  passage  which  may  shed  more 
light  upon  this  aspect  of  the  matter:  ''Land  is  used  for  other  pur- 
poses than  agriculture,  ....  and  when  so  used  yields  a  rent. 
....  The  ground  rent  of  a  house  in  a  small  village  is  but  little 
higher  than  the  rent  of  a  similar  patch  of  ground  in  the  open 
fields,  but  that  of  a  shop  in  Cheapside^  will  exceed  these,  by  the 
whole  amount  at  which  people  estimate  the  superior  facilities  of 
money-making  in  the  more  crowded  place."^  But  all  this  hardly 
explains  why  Cheapside  came  to  be  Cheapside !  Why  did  Cheap- 
side  happen  to  become  a  "favorable"  location?  A  theory  of  lo- 
cation will  consider  the  situation  or  location  rent  a  problem 
rather  than  merely  a  fact,  and  therefore  the  theory  of  location 
may  serve  as  a  fruitful  avenue  of  approach  to  certain  obscure 
aspects  of  the  theory  of  rent,  value,  and  distribution.  We  shall 
have  occasion  later  to  indicate  briefly  how  it  becomes  important 
for  the  theory  of  monopoly,  for  the  theory  of  international  trade, 
and  for  the  theory  of  railway  rates.  While  it  would  be  interest- 
ing to  consider  here  Mill's  analysis  of  the  influence  of  the  prog- 
ress of  industry  upon  rents,^^  we  shall  have  to  content  ourselves 
with  a  mere  mention  of  the  problem  and  proceed  to  a  few  obser- 
vations upon  the  position  of  Alfred  Marshall. 

The  strong  interest  of  Marshall  in  production  naturally  led 
him  to  touch  upon  the  question  of  what  causes  the  location  (or, 
as  he  called  it,  ''localisation")  of  industries  to  change.  From  the 
point  of  view  of  anyone  interested  in  the  history  of  economic 
ideas  in  general  and  in  the  history  of  the  theory  of  location  in 
particular  it  is  quite  interesting  that  Alfred  Marshall  (in  the  in- 
troduction to  the  first  edition  of  his  Principles  of  Economics) 
acknowledges  his  great  indebtedness  to  Thünen.  It  will  be  re- 
membered that  it  was  Thünen  who  advanced  a  theory  of  the  lo- 

^  An  expensive  trading  section  in  London. 
^Principles,  III,  chap,  v,  3;  cf.  also  III,  chap,  v,  4. 
^"  Principles,  IV,  chap.  iii. 


cation  of  agricultural  production/^  But  while  Thünen  related 
his  theory  very  definitely  to  his  theory  of  rent,  modifying  the 
position  of  Adam  Smith/"  Marshall  did  not  approach  this  prob- 
lem of  location  from  a  theoretical  point  of  view,  and  consequent- 
ly attempted  no  answer  to  that  aspect  of  the  theory  of  rent  which 
we  have  just  pointed  out.  There  is  a  twofold  explanation  for  this. 
For  one  thing,  Marshall's  main  effort  was  directed  toward  work- 
ing into  the  theory  of  rent  the  supposedly  new  equilibrium  theory 
of  demand  and  supply,^^  contenting  himself  with  carefully  restat- 
ing the  theory  that  ''rent  does  not  enter  the  cost  of  production,"^* 
Marshall  does  not  inquire  into  the  problem  which  he,  like  Mill 
before  him,  encounters.  In  discussing  the  argument  which  arose 
between  Ricardo  and  Smith  regarding  the  ''price  at  which  coals 
can  be  sold  for  any  considerable  time,"^^  he  is  inclined  to  agree 
with  Ricardo  that  "it  is  the  least  fertile  mine  which  regulates  the 
price."  Omitting  the  matter  of  a  royalty  which  enters  on  account 
of  the  exhaustibility  of  a  mine,  Marshall,  like  Mill,  does  not  ex- 
plain why  a  less  fertile  mine  should  be  in  use  at  all.  Like  Mill, 

"  Der  Isolierte  Staat,  particularly  Part  I.  For  a  recent  interpretation  of  the 
significance  of  this  treatise  in  the  history  of  economic  thought,  cf.  Edgar  Salin, 
"Der  Isolierte  Staat  1826-1926,"  in  Zeitschrift  für  die  gesamte  Staatswissen- 
schaft, 1926. 

"  He  made  the  distinction  between  rent  of  land  and  profit  on  capital  in- 
vested on  the  land,  like  Ricardo. 

"  While  this  name  was  not  used  by  Mill,  the  essential  aspects  of  the  con- 
cept of  "equilibrium,"  as  far  as  they  matter  for  the  problem  here  in  hand,  were 
treated  by  Mill  as  indicated  above, 

"  It  is  stated  as  follows :  "When  land  capable  of  being  used  for  producing 
one  commodity  is  used  for  producing  another,  the  price  of  the  first  is  raised  by 
the  consequent  limitation  of  its  field  of  production.  The  price  of  the  second  will 
be  the  expense  of  production  (wages  and  profits)  of  that  part  of  it  which  only 

just  pays  its  way And  if  for  the  purposes  of  any  particular  argument  we 

take  together  the  whole  expenses  of  the  production  on  that  land,  and  divide  these 
among  the  whole  commodity  produced,  then  the  rent,  which  ought  to  count  in, 
is  not  that  which  the  land  would  pay  if  used  for  producing  the  first  commodity, 
?)Ut  that  which  it  does  pay  when  used  for  producing  the  second"  {Principles,  4th 
ed.,  p.  483). 

"  Cf.  loc.  cit.,  p.  484. 


he  speaks  of  the  fact  that  a  rise  in  rent  may  cause  a  manufac- 
turer to  move  into  another  town  or  into  the  country,  but  he  does 
not  say  why  the  rent  does  rise  in  the  first  instance.  Similarly,  he 
explains  that  the  demand  for  exceptionally  valuable  urban  land 
comes  from  traders  of  various  kinds,  wholesale  and  retail,  more 
than  from  manufacturers.  But  why  such  increase  in  the  demand 
should  come,  he  does  not  explain  at  all.  Still,  the  most  striking 
instance  where  Marshall  encounters  the  problem  of  location  (or 
situation)  without  undertaking  to  solve  it  is  in  his  discussion  of 
what  he  calls  situation  rent.^^ 

If  in  any  industry,  whether  agricultural  or  not,  two  producers  have 
equal  facilities  in  all  respects,  except  that  one  has  a  more  convenient  situa- 
tion than  the  other,  and  can  buy  or  sell  in  the  same  markets  with  less  cost 
of  carriage,  the  differential  advantage  which  his  situation  gives  him,  is  the 
aggregate  of  the  excess  charges  for  cost  of  carriage  to  which  his  rival  is  put. 
And,  we  may  suppose,  that  other  advantages  of  situation,  such,  for  instance, 
as  the  near  access  to  a  labour  market  especially  adapted  to  his  trade,  can  be 
translated  in  like  manner  into  money  values.  When  this  is  done  for,  say,  a 
year,  and  all  are  added  together  we  have  the  annual  money  value  of  the  ad- 
vantages of  situation  which  the  first  business  has  over  the  second;  and  the 
corresponding  difference  in  the  incomes  derived  from  the  two  businesses  is 
commonly  regarded  as  a  difference  of  situation  rent}"^ 

But  why  does  not  the  second  manufacturer  move  to  the  more 
favorable  location?  This  fact  certainly  needs  an  explanation! 
In  a  footnote  Marshall  refers  to  two  examples,  in  both  of  which 
the  competitive  position  of  two  productive  units  is  the  same 
because  the  additional  cost  of  production  due  to  capital  and 
labor  of  one  are  compensated  for  by  the  more  favorable  loca- 
tion of  the  other  in  relation  to  the  market.  "Favorable  loca- 
tion" in  both  cases  refers  to  advantages  in  transportation  costs. 
But  these,  obviously,  are  not  examples  of  production  which 
have  any  bearing  upon  the  problem  of  location,  because  when 

^^  Principles,  V,  chap.  x. 

"  The  italics  in  this  quotation  are  mine. 


locational  advantages  of  one  kind  (labor,  etc.)  are  balanced  by 
locational  advantages  of  another,  no  change  of  location  will  take 
place.  On  the  other  hand,  it  is  not  clear  how  the  advantage  due 
to  reduced  transportation  costs  can  be  called  a  "rent,"  since  it 
is  not  explained  why  the  other  productive  unit  is  not  quite  free 
to  go  to  a  place  with  the  same  balance  of  advantage/*  Feeling 
perhaps  the  inconclusiveness  of  his  reasoning,  Marshall  pro- 
ceeds to  treat  of  "exceptional  cases  in  which  the  income  derived 
from  advantageous  situation  is  earned  by  individual  effort  and 
outlay."  Much  of  this  uncertain  generalizing  could  have  been 
subjected  to  rational  explanation  by  an  adequate  understanding 
of  the  underlying  locational  problem.  It  remains  to  say  a  word 
regarding  certain  forms  of  quasi-rent  (as  Marshall  called  it) 
which  are  due  to  the  fact  that  a  certain  location  is  made  more 
favorable  by  environmental  factors.  The  true  nature  of  rents  of 
this  kind,  which  are  due  to  a  disturbed  equilibrium  of  loca- 
tions, becomes  recognizable  only  if  the  locational  network  of 
the  underlying  regular  stratum  of  locations  is  distinguished 
quite  clearly. 

Marshall's  reluctance  to  undertake  their  analysis  in  con- 
nection with  these  rent  problems  does  not,  however,  prevent  him 
from  treating  "the  concentration  of  specialized  industries  in 
particular  localities."^^  But  what  he  gives  is,  as  Alfred  Weber 
pointed  out  later,  a  more  or  less  systematic  survey  of  various 

^*The  actual  examples  refer  to  extractive  industries.  These  involve  the 
question  of  increased  output,  as  did  the  example  of  Mill  we  have  cited.  It  is 
curious  that  Marshall  should  at  this  point  quote  Thünen's  Der  Isolierte  Staat 
with  outspoken  approval,  while  failing  to  make  use  of  Thünen's  theory  of  loca- 
tion contained  therein. 

"  Principles,  IV,  chap.  x.  Cf .  also  his  interesting  discussion  in  Industry  and 
Trade  (1923),  chap,  ii,  and  elsewhere,  where  he  quotes  Alfred  Weber  (p.  27). 
But  it  seems  rather  doubtful  whether  he  appreciated  the  full  significance  of 
Weber's  theory,  since  he  says  of  it  that  it  is  a  development  of  Lardner's  Law  of 
Squares  in  transport  and  trade  (as  set  forth  in  Railway  Economy  [1850],  p.  14). 
The  connection  is  rather  far  fetched,  to  say  the  least. 


locational  factors;  but — much  like  Roscher-^ — ^he  does  not  in 
any  way  develop  or  even  employ  the  theoretical  concepts  which 
Thiinen  had  first  worked  out.  This  is  rather  interesting  (or  shall 
I  say  astonishing?)  in  view  of  the  close  relation  between  him 
and  Thiinen.  But,  as  has  been  noted  before,  Marshall  seems 
mainly  concerned  with  working  into  the  classical  system  the 
new  equilibrium  theory  which  is  also  to  be  found  in  Thiinen. 
Marshall  was  probably  too  deeply  concerned  by  the  "psycholog- 
ical" foundation  which  he  and  others  had  given  to  that  theory 
to  be  willing  to  bother  with  Thiinen 's  concept  of  an  isolated  eco- 
nomic system.^^  It  may  be  helpful,  therefore,  to  sketch  in  a  few 
sentences  the  main  outline  of  Thiinen's  theory  of  location,^^  al- 
though it  involves  in  some  respects  repeating  what  is  known  to 
economists  in  connection  with  his  theory  of  rent. 

Thiinen,  like  Ricardo,  studied  an  imagined  state  of  facts  in 

^**W.  Roscher,  Studien  ueber  die  Naturgesetze,  welche  den  natürlichen 
Standort  der  Industriezweige  bestimmen.  Similar  catalogues  of  possible  factors 
have  been  published  by  others,  compare,  for  example,  F.  S.  Hall,  "The  Localiza- 
tion of  Industries,"  Twelfth  Census,  Manufacturers,  Part  I ;  and  Edward  A.  Ross, 
"The  Location  of  Industries,"  Quarterly  Journal  of  Economics,  X  (1896),  247  ff. 
For  a  discussion  of  these  and  many  other  minor  contributions  cf.  Witold  Krzy- 
zanowski,  "Literature  of  Location  of  Industries,"  in  Journal  of  Political  Econ- 
omy, XXXV  (1927),  278  ff. 

^^  It  is  rather  hard  to  withstand  the  temptation  to  take  up  this  aspect  in  the 
history  of  economic  thought  in  greater  detail ;  but  such  an  undertaking  could  not 
be  given  justice  within  the  scope  of  this  brief  essay.  Similar  considerations  com- 
pel me  to  pass  over  without  more  than  a  casual  reference  the  difficult  problems 
which  arise  from  the  twelfth  chapter  of  the  sixth  book  of  Marshall's  Principles 
where  he  deals  with  the  influence  of  progress  on  value.  Such  further  discussion 
would  have  afforded  an  opportunity  to  consider  the  work  of  some  of  the  writers 
of  the  next  generation,  particularly  A.  C.  Pigou  and  J.  M.  Clark  (Principles  of 
Overhead  Costs). 

^His  theory  is  to  be  found  in  Der  Isolierte  Staat,  2d  ed.,  1842,  and  later. 
Edgar  Salin,  writing  upon  the  history  of  economic  theory,  expressed  the  belief 
that  Thiinen  was  the  most  important  German  theorist  of  the  nineteenth  century. 
However,  the  part  of  his  system  in  which  he  expounds  his  theory  of  location  has 
least  been  heard  of  and  is  seldom  referred  to  in  any  theoretical  treatises  written 
in  English.  Not  even  special  studies  such  as  that  of  Ross  mentioned  in  footnote 
20  above,  seem  to  have  been  aware  of  it. 


which  all  nonessential  aspects  of  the  real  case  have  been  elimi- 
nated. In  his  totally  isolated  economic  system-^  he  finds  that  the 
location  of  different  kinds  of  agricultural  production  is  deter- 
mined by  the  relation  between  the  price  of  the  products  in  the 
market  place  and  the  distance  from  the  market  place.  The  most 
significant  result  of  this  approach  to  the  problem  is  that  the  cost 
of  transporting  the  products  to  the  market  place  is  isolated  as  the 
basic  element  and  made  the  starting-point  of  the  analysis  of  lo- 
cation. It  is  possible  to  do  this  because  it  is  supposed  anyway 
for  the  purpose  of  this  analysis  that  labor  cost  (wages)  are  equal 
throughout  the  plain.^*  Besides,  equal  fertility  is  assumed 
throughout.  It  is  worth  noting  that  Thünen  does  not  consider 
the  effect  of  the  cost  of  transporting  appliances  (such  as  plows, 
etc.)  to  the  place  of  production.  This  omission  unduly  simph- 
fies  his  analysis  as  compared  with  that  of  Alfred  Weber.  But  it 
should  not  be  forgotten,  anyhow,  that  the  theory  of  location  of 
Thünen  was  the  by-product  of  quite  a  different  problem,  name- 
ly, "how  will  the  kind  of  agricultural  production  of  a  certain 
farm  be  affected  by  a  gradual  decline  of  the  prices  of  its  produce 
in  its  [fixed]  market" ?^^  It  is  well  known  that  Thünen  finds 
rent  to  be  due  primarily  to  the  advantage  which  is  caused  by  a 
smaller  distance  from  the  consuming  center,  i.e.,  smaller  costs 
of  transportation.^^  This  finding  is  based  upon  the  law:  'The 
value  of  produce  at  the  place  of  production  decreases  with  the 
distance  of  the  place  of  production  from  the  market  place.""^ 

^^  The  picture  of  this  system  is  well-known.  He  supposes  a  town  (market 
place)  within  a  fertile  plain,  without  navigable  rivers  or  canals,  and  of  given  fer- 
tility throughout,  which  ends  somewhere  far  away  from  the  town  in  the  wilder- 
ness. Thünen  himself  calls  this  ".  .  .  .  eine  bildliche  Darstellung,  eine  Form,  die 
den  Ueberbhck  erleichtert  und  erweitert;  die  wir  aber  nicht  aufgeben  dürfen, 
weil  sie,  wie  die  Folge  ergeben  wird,  so  reich  an  Resultaten  ist." 

^This  supposition,  while  not  expressly  made  in  the  first  part,  is  noted  by 
Thünen  in  the  third  part,  p.  73. 

^  Der  Isolierte  Staat,  I,  p.  21. 

"*  Op.  cit.,  p.  227.  ''  Op.  cit.,  p.  37. 


But  Thiinen  was,  of  course,  well  aware  of  the  fact  that  this  is  not 
a  complete  explanation  of  rent.  In  the  third  part  of  his  work  he 
finds  rent  based  upon  differences  in  the  wage  level.  This  second 
explanation  seems  to  contain  a  contradiction  to  the  first.  Such 
seeming  contradiction  is  due  to  different  premises;  in  the  one 
case  it  is  assumed  that  the  wage  level  is  constant;  in  the  other, 
that  the  value  of  the  produce  is  constant,  i.e.,  that  cost  of  trans- 
portation is  constant  (according  to  the  rule  just  cited).  It  is 
possible  to  assume  this  theoretically  in  spite  of  the  fact  that  the 
wage  level  is  changing — indeed,  this  possibiHty  is  of  central  im- 
portance for  all  that  follows.  This  second  assumption  that  the 
value  of  the  produce  is  constant  further  involves  the  assumption 
that  no  more  uncultivated  soil  is  available.  In  the  first  case, 
then,  the  value  of  the  produce  is  the  variable,  dependent  upon 
the  larger  or  smaller  costs  of  transportation  to  the  market  place. 
In  the  second  case,  the  wage  level  is  the  variable.  What  is  com- 
mon to  both  cases  is  that  the  cost  of  production  does  not  rise  in 
proportion  to  the  value  of  the  produce,  so  that  if  the  value  of  the 
produce  rises  above  a  certain  point  there  remains  a  surplus 
which  is  the  basis  of  a  rent.^^  Expressing  this  finding  in  relation 
to  the  main  problem  before  referred  to,  Thiinen  formulates 
(stated  with  slight  alterations  for  the  present  purpose)  that  the 
price  of  the  produce  must  be  so  high  that  the  rent  of  that  farm 
for  which  it  is  most  expensive  to  transport  the  produce  to  the 
market  place  does  not  become  less  than  zero.  Unfortunately, 
Thunen  did  not  work  out  the  significance  of  this  second  aspect 
for  his  implied  theory  of  location.  It  would  have  been  necessary 
to  analyze  the  variations  produced  by  the  introduction  of  this 
second  factor:  labor  cost.  Had  he  done  so,  his  theory  would  be 
more  clearly  related  to  that  of  Alfred  Weber.  It  will  be  ob- 
served that  Thunen,  considering  agricultural  production  only 
(an  extractive  industry),  assumes  here  a  definite  and  constant 
limit  of  production  at  any  given  place  (so  and  so  many  bushels 

^Der  Isolierte  Staat,  I,  p.  73. 


of  wheat  per  acre,  for  example).  The  validity  of  this  assump- 
tion is,  even  in  agriculture,  subject  to  the  further  assumption 
^  that  the  most  intensive  methods  are  already  in  use  equally 
throughout.  Such  an  assumption  would  not  be  in  accord  with  the 
generally  accepted  modern  doctrine  of  the  variability  of  produc- 
tive forces.  Be  this  as  it  may,  such  supposition  has  obviously 
no  significant  application  to  manufacturing  industries.  It  is,  on 
the  contrary,  possible  to  assume  that  a  practically  unlimited 
amount  of  one  kind  of  production  may  be  carried  on  at  one  place 
rather  than  another.  More  of  this  later. 

I  have  said  before  that  Thünen's  theory  of  agricultural  loca- 
tion was  a  by-product  of  his  effort  to  determine  which  kind  of 
production  would  best  be  carried  on  at  a  given  place.  Alfred 
Weber,  on  the  other  hand,  undertakes  the  analysis  of  industrial 
location  for  its  own  sake.^^  It  is  useful  to  bear  this  difference  in 
mind.  Observing  the  gigantic  movements  of  manufacturing  in- 
dustries, Weber  asks:  What  causes  a  given  industry  to  move 
from  one  location  to  another?  What  are  the  general  economic 
laws  determining  these  movements  ?  Theoretically,  Weber,  like 
Thiinen,  might  have  asked:  Which  industry  should  be  carried 
on  at  any  given  place?  But,  as  a  matter  of  fact,  such  an  ap- 
proach to  the  problem  appears  mistaken  at  first  sight  because 
the  possibilities  of  manufacture  are  legion.  This  point  reveals  a 
third  limitation  of  Thünen's  analysis:  he  assumes  a  very  limited 
group  of  products,  namely,  the  agricultural  produce  of  German 
farms  in  the  beginning  of  the  nineteenth  century.  This  made  it 
possible  for  him  to  find  a  reasonably  satisfactory  answer  to  his 
question,  what  kind  of  production  would  best  be  carried  on  at  a 

^  Alfred  Weber,  TJeber  den  Standort  der  Industrien,  I.  Teil,  Reine  Theo- 
rie des  Standorts,  and  Alfred  Weber,  "Industrielle  Standortslehre  (Allgemeine 
und  kapitalistiche  Theorie  des  Standorts),"  in  Grundriss  der  Sozialökonomik, 
Abteilung  VI,  B.  The  few  points  which  are  emphasized  here  are  chosen  with  ref- 
erence to  the  focusing  point  of  this  essay,  rent.  They  do  not  propose  to  describe 
the  theory  itself.  That  will  best  be  understood  from  Weber's  own  work. 


given  place.  But  this  answer  is  satisfactory  only  within  the  lim- 
its just  indicated. 

Weber,  who  concentrates  upon  the  problem  of  location  as 
such,  is  not  hampered  by  this  limitation.  He,  of  course,  is  in- 
terested only  in  discovering  the  operation  of  such  general  fac- 
tors as  influence  manufacturing  industries.  But  before  going 
into  the  questions  connected  with  that  issue,  it  may  be  useful  to 
compare  the  theoretical  picture  from  which  he  starts  with  that 
of  Thünen.  Like  Thiinen,  he  assumes  an  absolutely  even  plain 
and  equal  transportation  rates  throughout.  But  he  does  not  as- 
sume one  consuming  center;  he  assumes  many  of  them  scat- 
tered over  the  plain.  Instead  of  equal  fertility  throughout, 
which  would  correspond  to  equal  amounts  of  fuel  and  raw  mate- 
rials at  equal  cost  throughout,  Weber  assumes  only  equal  cost  / 
of  fuel  and  raw  materials  at  all  deposits,^^  but  retains  the  un- 
even distribution  of  such  deposits.  These,  and  these  only,  are 
Weber's  assumptions. 

The  variable  general  factors  are  of  two  kinds :  those  which 
are  primary  causes  of  the  regional  distribution  of  industry  (re- 
gional factors),  and  those  which  are  secondary  causes  of  a  re- 
distribution of  industry  (agglomerating  and  deglomerating  fac- 
tors), being  themselves  effects  of  those  regional  factors.  By  ana- 
lyzing one  given  industrial  process  Weber  deductively  finds  two 
general  regional  factors  of  cost:  transportation  costs  and  labor 
costs.  It  might  be  objected  here  that  transportation  costs  are 
themselves  partly  determined  by  labor  costs.  This  is  true;  but 
it  is  essential  for  the  analysis  of  location  to  isolate  costs  of  trans- 
portation as  a  separate  element,  since  the  problem  of  location  is 
one  of  spatial  distribution.  The  term  ''labor  costs"  is  therefore 
used  here  and  elsewhere  in  the  sense  of  labor  costs  as  applied  to 

^"  When  Weber  wishes  to  express  possible  differences  in  the  price  of  fuel  and 
raw  materials  at  different  deposits  by  additions  to  the  distance  between  them 
and  the  place  of  production,  this  amounts  theoretically  to  assuming  equal  cost 
of  fuel  and  raw  material  throughout  at  their  deposits,  since  the  theoretical  prem- 
ises contain  no  assumption  regarding  the  "real"  distance  of  any  point. 



a  given  industry.  This  simplification  is  justified  by  the  fact  that 
Weber's  problem  is:  What  causes  a  given  industry  to  move/ 
from  one  location  to  another?  It  is  even  possible  to  assume  va- 
riations in  the  wage  level  (labor  costs)  of  such  a  given  industry 
without  necessarily  implying  a  change  in  the  labor  costs  of  any 
other  industry,  like  the  transporting  agency.  Apparently  these 
are  exactly  the  same  factors  which  Thünen  had  found.  But,  un- 
like Thünen,  Weber  analyzes  the  effects  of  a  change  in  both 
variables.  After  having  ascertained  the  laws  determining  the  lo- 
cation when  labor  costs  are  constant,  he  proceeds  to  ascertain 
the  alterations  resulting  from  varying  costs  of  labor.  He  is  able 
to  formulate  his  result  in  definite  rules.  Firstly,  he  finds  that  the\/ 
location  of  manufacturing  industries  is  determined  (transporta- 
tion costs  being  variable,  labor  costs  constant)  by  the  ratio  be- 
tween the  weight  of  localized^'^  material  and  the  weight  of  the 
product.^-  This  ratio  Weber  calls  the  material  index.  The  ex- 
planatory value  of  this  general  rule  need  not  be  discussed  here 
in  detail.^^  This  result  was  reached  upon  the  assumption  of 
equal  labor  costs  throughout.  What  variations  will  be  caused 
by  varying  costs  of  labor?  Weber  finds:  The  extent  of  the 
variation  caused  by  varying  labor  costs  is  determined  by  the 
ratio  between  cost  of  labor  per  ton  of  product  (labor  index)  and 
the  total  weight  of  all  goods  (product,  materials,  fuel,  etc.) 

^^  Localized  are  such  materials  as  are  not  to  be  had  everywhere ;  the  latter 
are  called  ubiquities.  Cf.  infra,  p.  51.  An  interesting  discussion  of  these  concepts 
will  be  found  in  Oskar  Engländer,  Theorie  des  Güterverkehrs  und  der  Fracht- 
sätze, p.  121  ff.  It  is  convincingly  urged  there  that  the  decisive  point  is  whether 
a  material  is  to  be  had  everywhere  at  equal  prices. 

^^It  is  fairly  simple  to  relate  this  rule  to  the  theory  of  land  rent  as  it  be- 
comes a  function  of  location.  A  fuller  discussion  will  be  undertaken  below  in 
connection  with  the  indirect  general  agglomerating  and  deglomerating  factors 
determining  the  location  of  manufacturing  industries. 

^'  By  way  of  illustration,  this  may  be  said :  Certain  materials  enter  with 
their  entire  weight  into  the  product  (silver,  etc.);  others  not  at  all  (coal,  etc.). 
This  distinction  is  of  considerable  significance.  Weber  is  able  to  make  the  for- 
mula that  the  production  of  all  industries  whose  material  index  is  not  greater 
than  I  is  located  at  the  place  of  consumption  (cf.  infra,  p.  61). 


transported.  This  total  weight  is  called  locational  weight,  and 
the  ratio  just  described  is  called  labor  coefficient.  Now  Weber 
can  deduce  the  second  general  rule:  When  labor  costs  are  varied,  '^ 
an  industry  deviates  from  its  transport  locations  in  proportion 
to  the  size  of  its  labor  coefficient. 

The  writer  wishes  Alfred  Weber  had  analyzed  the  locations 
which  result  when  transportation  costs  are  eliminated,  before 
studying  the  variations  due  to  varying  labor  costs,  while  cost  of 
transportation  remained  variable.^*  The  results  of  such  an  anal- 
ysis would  enable  us  to  check  upon  the  results  of  the  previous 
analysis  by  introducing  transportation  costs  into  a  network  of 
locations  first  solely  determined  by  cost  of  labor.^^  It  would 
have  served  also  as  an  excellent  basis  of  defense  against  the  crit- 
icism of  Werner  Sombart,'^^  which  does  not  really  touch  the 
foundation  of  Weber's  theory  at  all  because  Sombart  does  not 
take  up  the  problem  from  the  point  of  view  of  economic  theory. 
It  is  not  possible  to  go  into  details,  but  the  final  result  of  such  an 
analysis  seems  quite  obvious.  If  transportation  costs  were  con- 
stant, all  production  would  go  to  the  locations  with  lowest  labor 
costs.  To  illustrate  this  "rule"  let  us  assume  that  the  labor  costs 
are  equal  at  A,  B,  and  C,  and  a  given  distribution  of  a  given  in- 
dustry between  A,  B,  and  C  exists.  If,  then,  the  labor  costs  at  A 
fall,  all  production  will  move  at  once  from  B  and  C  to  A  .^^  It 

^  It  is  necessary  for  a  clear  understanding  of  this  discussion  to  bear  in  mind 
that  an  elimination  of  transportation  costs  would  only  result  if  it  were  assumed 
that  it  costs  the  same  to  ship  goods  of  any  kind  and  any  weight  any  distance. 

^'  It  will  be  remembered  that  Thiinen  made  this  first  step,  although  incom- 
pletely, due  probably  to  his  preoccupation  with  the  problem  of  rent  (cf.  above, 
p.  xviii).  But  he  failed  to  carry  his  analysis  beyond  this  elemental  stage  and  did 
not  study  either  the  variations  caused  by  introducing  labor  costs  into  a  system 
of  locations  determined  by  transportation  costs  or  the  variations  caused  by  in- 
troducing transportation  costs  into  a  system  determined  by  labor  costs. 

^  Cf .  his  review  in  the  Archiv  für  Sozialwissenschaft  und  Sozialpolitik,  XXX 
(1910),  748,  and  Der  Moderne  Kapitalismus,  3d  ed..  Vol.  II,  2,  p.  800,  901  ff. 

'^  It  must  not  be  objected  here  that  this  is  inconceivable,  because  the  "de- 
mand" for  labor  in  A  would  at  once  raise  the  cost  of  labor  in  A,  since  it  is  an 


would  be  easy  to  show  that  an  introduction  of  transportation 
costs  into  these  simple  equations  would  give  results  identical 
with  those  obtained  by  Weber.  Obviously  the  rule  just  stated,  if 
we  should  be  willing  to  call  it  such,  has  no  explanatory  value, 
because  its  application  to  different  industries  shows  no  "typi- 
cal" alterations  for  each  industry,^^  but  affects  all  industries 
ahke;  whether  they  had  high  labor  costs  per  ton  of  product,  or 
low,  they  would  obviously  go  to  the  location  which  rendered  this 
part  of  their  cost  lowest. 

The  main  reason  for  entering  upon  the  discussion  contained 
in  the  foregoing  paragraph  is  to  show  that  Weber  was  methodo- 
logically fully  justified  in  starting  his  analysis  with  variable 
transportation  costs  and  constant  labor  costs,  because  the  loca- 
tional  significance  of  variations  in  labor  costs  becomes  capable 
of  analysis  only  in  its  relation  to  the  total  weight  of  all  goods  to 
be  transported  during  the  particular  process  of  production.  It 
seems  to  the  writer  that  it  is  of  the  greatest  importance  that  Al- 
fred Weber  has  thus  succeeded  in  laying  bare  the  fact  that  trans- 
portation costs  are  theoretically  the  most  fundamental  element 
determining  location,  because  it  is  only  in  relation  to  these 
two  fundamental  figures,  the  material  index  and  the  locational 
weight,  that  general  rules  can  be  stated  whose  application  to 
particular  industries  shows  significant  alterations  for  each  in- 
dustry.^^  The  only  question  which  arises  regarding  Weber's  de- 
ductions is  whether  it  would  not  have  been  better  to  stick  to 
transportation  costs  as  the  only  ''general"  factor  of  location, 
and  to  treat  labor  as  an  indirect  factor.  Andreas  Predöhl  seems 
to  be  inclined  to  take  this  view,  although  his  claim  that  "there  is 

implication  of  our  hypothesis  that  there  is  an  abundant  supply  of  labor  at  every 
location  at  the  prevailing  wage  level. 

^®  This  may  be  the  reason  why  Thünen  refrained  from  stating  it  in  relation 
to  the  problem  of  location. 

^^This  entire  reasoning  is  based  upon  a  theory  of  theory  which  chooses 
among  different  possible  theories  upon  the  basis  of  their  explanatory  value. 


no  logical  difference  between  the  labor  factor  and  any  other  local 
factor"  goes  too  far.*° 

What  has  been  said  thus  far  may  suffice  to  explain  the  loca- 
tion of  industries  as  affected  by  factors  which  are  both  common 
to  all  industries  (general  factors)  and  direct  in  their  operation. 
But,  as  was  noted  before,  certain  further  variations  are  caused 
by  factors  which  are  themselves  partly  caused  by  those  direct 
or  primary  (Weber  calls  them  regional)  factors  just  discussed. 
These  indirect  factors  (agglomerating  and  deglomerating)  are 
not  capable  of  the  same  deductive  analysis  as  the  direct  fac- 
tors discussed  before,  because  they  follow  from  the  social  na- 
ture of  production.  Quite  generally  speaking,  such  an  indirect 
factor  is  an  advantage  which  follows  from  the  fact  that  not 
less  than  a  certain  quantum  of  production  is  agglomerated  at 
one  place  (agglomerating  factor),  or  from  the  fact  that  not 
more  than  a  certain  quantum  of  production  is  agglomerated  at 
one  place  (deglomerating  factor).  The  agglomerating  factors 
(advantages  from  large-scale  production  through  technical  ap- 
paratus, labor  organization,  etc.)  are  related  to  the  nature  of 
the  particular  industry,  while  the  deglomerating  factors  are  all 
traceable  to  the  inevitable  increases  in  the  rent  of  land  which  ac- 
company the  agglomeration  of  industry. 

How  far,  then,  will  agglomeration  go?  The  significance  of 
an  answer  to  this  question  for  an  understanding  of  rent  is  ob- 
vious. Let  us  follow  Weber's  analysis.  He  returns  to  the  as- 
sumption of  constant  labor  costs  in  order  to  study  the  deviations 
caused  by  these  agglomerating  and  deglomerating  factors  with- 
in the  network  of  locations  as  determined  by  costs  of  transpor- 
tation alone.  He  eliminates  the  deglomerating  factors  by  treat- 
ing them  as  lessening  the  force  of  agglomerating  factors.  But, 

*°  Cf.  his  "The  Theory  of  Location  in  Its  Relation  to  General  Economics," 
Journal  of  Political  Economy,  Vol.  XXXVI  (1928),  where  he  bases  his  arguments 
to  some  extent  upon  Alfred  Marshal;  and  "Das  Standortsproblem  in  der  Wirt- 
schaftstheorie," Weltwirtschaftliches  Archiv  (1925),  XXI,  where  he  bases  his  ar- 
guments upon  Gustav  Cassel. 


according  to  Weber,  this  can  only  be  assumed  as  long  as  isolated 
industries  are  considered;  otherwise  there  exists  the  possibility 
of  ^'accidental"  agglomeration  of  several  different  industries, 
which  would  create  deglomerating  tendencies  quite  apart  from 
an  agglomeration  of  any  particular  industry.*^  This  leads  Weber 
to  consider  the  effect  of  the  agglomerating  factors  upon  an  iso- 
lated industry,  whose  locations  have  been  determined  by  the 
costs  of  transportation.  The  economies  per  ton  of  product  for 
each  quantum  of  agglomeration  constitute  a  function  of  the  ag- 
glomerating factors,  the  ''function  of  economy."  The  increases 
of  the  economies  from  quantum  to  quantum  constitute  another 
function  of  the  agglomerating  factors,  the  "function  of  agglom- 
eration." This  latter  function  is  the  real  measure  for  the  extent 
of  agglomeration.  The  extent  of  agglomeration  is  determined  by 
the  ratio  between  this  function  of  agglomeration  and  the  loca- 
tional  weight,  the  latter  multiplied  by  the  (uniform!)  rate  of 
transportation.  Weber  finds  that  a  formula  exists  which  shows 
which  quantum  of  agglomeration  will  be  realized.^- 

The  reintroduction  of  variable  labor  costs  shows  the  two 
"deviating"  tendencies,  labor  and  agglomeration,  competing 
with  each  other,  with  the  result  that  the  tendency  of  industry  to 
concentrate  at  a  few  locations  will  be  further  increased.  This 
finding  would  support  our  earlier  suggestion  regarding  the  posi- 
tion of  labor  costs  within  a  theoretical  treatment  of  location. 

The  foregoing  may  suffice  to  show  that  Alfred  Weber  and 
Thünen  both  point  out  the  fundamental  importance  of  trans- 
portation costs  for  any  theoretical  understanding  of  location. 
Hence,  upon  the  basis  of  the  assumptions  made  in  the  beginning, 

^  The  writer  is  wondering  whether  it  can  even  then  be  assumed.  Labor 
costs,  we  saw,  may  concentrate  a  given  industry  in  one  or  two  places  which 
would  create  these  deglomerating  tendencies.  As  a  matter  of  fact,  even  when 
only  transportation  costs  are  variable,  a  concentration  of  industries  in  one  loca- 
tion may  cause  a  sufficient  rise  in  rent  to  "deglomerate"  them.  This  was  pointed 
out  partly  and  from  another  point  of  view  by  Predöhl,  loc.  cit. 

*"  CL  infra,  p.  153  Ü. 


rent  is  capable  of  analysis  as  a  function  of  location.^^  It  is  at 
this  point,  the  writer  believes,  that  the  importance  of  the  theory 
of  location  for  general  economic  theory  becomes  apparent,  for  it 
was  in  connection  with  this  problem  that  Thiinen  developed 
whatever  theory  of  location  he  did  develop. 

Among  the  problems  which  have  presented  major  difficulties 
to  economic  theory,  the  effect  of  forces  operating  to  restrain  trade 
has  occupied  a  very  important  place.  Monopolies,  transporta- 
tion rates,  and  international  tariffs  stand  out  among  such  forces. 
Their  separate  theories  must  necessarily  be  interrelated.  The 
connecting  link  between  them  is  an  adequate  theory  of  rent. 

As  to  the  theory  of  monopoly,  I  shall  venture  no  more  than  a 
hint.  A  more  elaborate  discussion  would  necessitate  an  analysis 
of  the  work  of  at  least  A.  C.  Pigou  and  J.  M.  Clark.**  But  one 
thought  suggests  itself  at  once:  if  all  deglomerating  tendencies 
are  related  to  the  rise  of  land  value,  i.e.,  rents,  then,  where  no 
rise  in  land  values  becomes  apparent  (let  us  say  in  a  socialist 
system),  the  result  would  seem  to  be  a  considerable  acceleration 
of  agglomeration.*^  But  most  economists  today  would  hold  that 

*^  Predöhl,  loc.  cit.,  suggests  a  threefold  basis  of  location  for  the  purpose  of 
a  general  theory  of  location :  rent,  other  local  cost  as  a  whole,  and  transporta- 
tion cost.  But  if  rent  is,  as  I  think  was  shown  sufficiently,  a  function  of  location, 
it  is  theoretically  quite  unsatisfactory  to  assume  it  as  a  general  or  direct  "fac- 
tor" of  location.  This  aspect  of  Predöhl's  arguments  was  also  questioned  by  O. 
Engländer  (although  from  another  viewpoint),  "Kritisches  und  Positives  zu 
einer  allgemeinen  reinen  Lehre  vom  Standort,"  Zeitschrift  für  Volkswirtschaft 
und  Sozialpolitik,  Vol.  V,  Nos.  7-9  (1926),  and  Predöhl's  reply,  "Zur  Frage  einer 
allgemeinen  Standortstheorie,"  Zeitschrift  für  Volkswirtschaft  und  Sozialpolitik, 
Vol.  V,  Nos.  10-12  (1927). 

"  Cf .,  for  example,  J.  M.  Clark,  Economics  of  Overhead  Costs,  particu- 
larly pp.  82-83. 

^^  I  do  not  know  hov/  much  weight  can  be  attached  to  Russian  statistics  in 
matters  of  this  kind,  but  if  the  recent  census  is  fairly  correct,  the  development 
in  Soviet  Russia  seems  to  be  at  least  in  accordance  with  this  statement.  Cf.  For- 
eign Affairs,  VI,  333,  In  this  connection  it  is  amusing  to  note  that  Weber's  theory 
of  location  has  been  translated  into  Russian  in  recent  years  and  acquired  a  great 
vogue  in  that  country,  I  am  told.  The  independence  of  its  conclusions  from  the 
price  mechanism  lends  it  significance  there,  perhaps. 


since  rent  would  be  an  element  of  the  cost  of  production  in  a  so- 
cialist state,  such  an  acceleration  would  be  impossible  in  the  long 
run,  and  that  the  final  equilibrium  would  be  identical.  However, 
what  has  been  said  about  the  locational  foundation  of  rent,  sug- 
gests a  more  complex  situation,  as  we  are  apparently  dealing 
with  interdependent  variables. 

In  applying  the  theory  of  location  to  the  theory  of  transport 
rates,  a  suggestive  start  has  been  made  by  Oskar  Engländer.  A 
good  deal  of  light  is  shed  also  upon  this  aspect  by  Stuart  R.  Dag- 

Finally  international  trade  was  taken  up  by  Alfred  Weber 
himself.*^  In  his  general  work  he  attacked  the  theory  of  the  'in- 
ternational division  of  labor,"  thus  taking  a  stand  opposed  to 
that  of  many  other  economists.*^  The  forces  which  seem  to  de- 
termine the  location  of  industries  would  obviously  permeate  the 
international  field,  and  this  led  Weber  to  apply  the  rules  which  he 
had  found  to  the  problems  of  international  trade.  One  might 
start  from  the  assumption  of  an  even  distribution  of  the  different 
kinds  of  production  over  the  entire  earth  rather  than  from  the 
assumption  of  the  ''international  division  of  labor."  The  classical 
doctrine  of  free  trade,  says  Weber,  takes  only  capital  and  labor 

*®  Cf .  his  The  Principles  of  Inland  Transportation  and  Oskar  Engländer, 
Theorie  des  Güterverkehrs  und  der  Frachtsätze. 

*~'  "Die  Standortslehre  und  die  Handelspolitik,"  Archiv  fuer  Sozialivissen- 
schajt  und  Sozialpolitik,  XXXII  (1911),  667  ff.  There  is  some  hope  that  this 
whole  aspect  of  the  theory  of  location  will  be  further  developed  soon.  Bertil  Oh- 
hn  has  recently  ventured  upon  the  bold  assertion  that  "the  theory  of  interna- 
tional trade  is  nothing  but  an  international  theory  of  location"  ("1st  eine  Mod- 
ernisierung der  Aussenhandelstheorie  erforderhch?"  Weltwirtschaftliches  Archiv, 
XXVI,  97  ff.).  It  does  not  become  very  clear  from  this  article,  unfortunately, 
how  Ohlin  expects  to  elaborate  upon  his  theme. 

**  Cf.,  for  example,  A.  B.  Clark  (in  Palgrave's  Dictionnry,  1923) :  "By  local- 
ization of  industry  is  meant  the  concentration  of  different  industries  in  different 
localities,  a  phenomenon  in  its  international  aspects  aptly  described  by  Torren's 
phrase  'territorial  division  of  labor.'  "  This  in  1923 ;  the  article  [on  localization] 
does  not  even  mention  the  Standort  der  Industrien." 


into  consideration  when  discussing  costs  of  production,  while  the 
''natural"  factors  are  supposedly  eliminated  by  the  Ricardian 
theory  of  rent.  This  approach  makes  it  impossible  to  appreciate 
the  independent  significance  of  the  costs  of  transportation.  The 
picture  of  the  "natural"  tendencies  of  the  distribution  of  eco- 
nomic forces  shows  really  four  stages  (or  layers) : 

1.  The  farming  population  will  be  distributed  rather  evenly 
around  the  historical  centers  of  culture  and  population  (Thii- 
nen's  belts). 

2.  All  industries  which  remain  so  oriented  under  the  influ- 
ence of  costs  of  transportation  (i.e.,  industries  which  use  more 
"pure"  materials  or  ubiquities  than  weight-losing  materials)  will 
be  evenly  distributed  upon  this  foundation. 

3 .  Industries  which  show  considerable  weight  losses  during 
the  process  of  production  will  be  attracted  to  the  deposits  of  raw 
materials  and  fuels. 

4.  Industries  with  high  labor  costs  per  ton  of  products  will 
be  concentrated  at  the  favorable  international  labor  markets. 

From  this  it  will  appear  that  the  classical  doctrine  (proba- 
bly upon  the  basis  of  actual  events  in  England  at  the  time)  con- 
centrated its  attention  upon  the  fourth  stage  and  attributed  to  it 
a  good  deal  of  what  was  probably  due  to  the  third.  However, 
there  is  a  certain  recognition  of  Weber's  point  of  view  (al- 
though, as  we  have  shown,  without  the  theoretical  foundation) 
in  Marshall.*^  Friedrich  List,  in  a  sense,  represents  a  reaction 

^Principles,  4  ed.,  p.  761.  "It  is  no  slight  gain  that  she  [England]  can  make 
cheaply  clothes  and  furniture  and  other  commodities  for  her  own  use ;  but  those 
improvements  in  the  arts  of  manufacture  which  she  has  shared  with  other  na- 
tions have  not  directly  increased  the  amount  of  raw  produce  which  she  can  ob- 
tain from  other  countries  with  the  product  of  a  given  quantity  of  her  own  cap- 
ital and  labor.  Probably  more  than  three-fourths  of  the  whole  benefit  she  has 
derived  from  the  progress  of  manufactures  during  the  present  century  has  been 
through  its  indirect  influence  on  lowering  the  transport  of  men  and  goods,  of 
water  and  light,  of  electricity  and  news;  for  the  dominant  economic  fact  of  our 
own  age  is  the  development,  not  of  the  manufacturing,  but  of  the  transport 


against  the  classical  overemphasis  upon  labor  costs  when  he  says 
that  wherever  there  is  agriculture  there  must  also  be  industry. 
But  he  does  not  undertake  to  construct  a  theoretical  foundation 
for  this  aspect  of  his  protest.  Only  upon  the  basis  of  an  adequate 
theory  of  location  is  it  possible  to  fit  the  two  points  of  view  into  a 
satisfactory  theoretical  harmony. 

It  seemed  primarily  desirable  to  point  out  the  significance 
of  isolating  costs  of  transportation  for  any  theory  of  location.  In 
spite  of  the  apparent  distortions  which  the  network  of  locations 
as  determined  by  transportation  costs  alone  is  subject  to  in  the 
international  field,  a  clear  analysis  of  the  working  of  this  fac- 
tor has  much  to  contribute  toward  a  deeper  understanding  of  the 
forces  underlying  the  international  distribution  of  industries."^ 
Weber's  new  approach  enables  him  to  restate  the  doctrine  of  free 
trade.  If  the  natural  evolution  tends  to  develop  new  industrial 
centers,  such  tendencies  may  be  retarded  or  accelerated,  but 
they  cannot  be  eliminated. 

To  summarize,  land  rents,  i.e.,  advantages  due  to  favorable 

industries.  It  is  these  that  are  growing  most  rapidly  in  aggregate  volume  and 
individual  power,  ....  they  also  which  have  done  by  far  the  most  toward  in- 
creasing England's  wealth."  (ItaHcs  mine.)  But  why?  If  the  costs  of  transpor- 
tation are  so  important,  their  operation  ought  to  be  given  the  appropriate  at- 
tention. That  this  whole  matter  is  in  some  way  related  to  the  question  of  land 
value  and  rent  is  also  asserted  by  Marshall :  "The  influence  on  values  which  has 
been  exerted  in  the  modern  age  by  the  means  of  transport  is  nowhere  so  con- 
spicuous as  in  the  history  of  land;  its  value  rises  with  every  improvement  in  its 
communications  with  markets  in  which  its  produce  can  be  sold,  and  its  value 

falls  with  every  new  access  to  its  own  markets " 

*°Says  Weber  (Archiv,  loc.  cit.,  p.  668):  "Jede  äussere  Handelspolitik  be- 
deutet, wenn  sie  einen  bewussten,  willkürlichen  Eingriff  in  das  natural  Gegebene 
darstellt,  den  Versuch,  Produktionszweige  in  einen  Wirtschaftskörper  hinein  und 
aus  anderen  herauszuziehen,  sie  in  ihrer  geographischen  Lagerung  zu  beeinflussen, 
zu  verschieben."  This  aspect  has  recently  been  expanded  upon  and  has  been  made 
the  basis  of  historical  systematization  of  the  problem  of  the  interrelation  between 
locational  development  and  the  growth  of  the  modern  state  by  Hans  Ritschl, 
"Reine  und  historische  Dynamik  des  Standorts  der  Erzeugungszweige"  in  Schmol- 
lers Jahrbuch,  Vol.  51,  pp.  813  ff. 


locations  of  industry  in  relation  to  raw  material  deposits  and 
market  areas,  appear  to  be  variable  functions  of  the  locations  of 
industry  which  are  in  turn  variable  functions  of  dynamic  (or 
creative)  factors,  such  as  the  development  of  new  material  re- 
sources, transportation  facilities,  or  increases  in  population  which 
determine  economic  development  in  the  long  run.  An  adequate 
theory  of  location  seems  bound  to  enrich  the  theory  of  land  rent 
and  thereby  perhaps  carry  repercussions  into  other  aspects  of 
the  theory  of  value. 

Carl  Joachim  Friedrich 


The  question  of  the  location  of  industries^  is  a  part  of  the 
general  problem  of  the  local  distribution  of  economic  activities. 
In  each  economic  organization  and  in  each  stage  of  technical 
and  economic  evolution  there  must  be  a  "somewhere"  as  well  as 
a  "somehow"  of  production,  distribution,  and  consumption.  It 
may  be  supposed  that  rules  exist  for  the  one  as  well  as  for  the 
other.  Still,  political  economy,  in  so  far  as  it  goes  beyond  the 
analysis  of  elemental  facts  and  beyond  pure  theory,  is  of  neces- 
sity primarily  description  and  theory  of  the  nature  of  economic 
organization  (Wirtschaftsart J.  The  presentation  and  theoreti- 
cal analysis  of  the  nature,  the  sequence,  and  the  juxtaposition  of 
the  different  kinds  of  economic  organization  is  its  natural  con- 
tent as  soon  as  it  attacks  concrete  reality.  This  is  such  an  enor- 
mous content  that  it  should  not  occasion  wonder  if  a  young  sci- 
ence, limiting  itself  in  its  initial  tasks,  treats  the  "somewhere" 
of  economic  processes  simply  as  a  function  of  the  nature  of  that 
process,  although  the  location  of  an  economic  process  is  only 
partly  a  function  of  its  nature.  In  other  words,  political  econo- 
mists have  dismissed  this  problem  of  location  with  some  general 
references  to  rules  of  local  and  international  division  of  labor, 
etc.,  or  political  economy  has  left  to  economic  geography  the 
theoretical  consideration  of  the  distribution  of  economic  proc- 
esses over  a  given  area.  Naturally,  the  latter  is  able  to  approach 
the  problem  only  in  so  far  as  it  can  be  explained  by  purely  phys- 
ical facts.  The  result  is  as  unsatisfactory  as  if  we  had  left  the 
analysis  of  the  nature  of  economic  processes,  i.e.,  political  econ- 
omy, to  the  technical  sciences. 

But  while  problems  of  location  have  been  treated  by  geogra- 

*  Industries  is  here  and  throughout  the  text  used  in  the  sense  of  manufactur- 
ing industries. — Editor. 


phers  primarily,  Thünen  is  a  notable  exception.  There  are,  too, 
several  later  attempts  in  this  field.  But  they  are  insignificant 
when  compared  with  the  magnitude  of  the  problem.  We  witness 
today  enormous  displacements  of  economic  forces,  migrations  of 
capital  and  human  labor  such  as  no  other  age  has  ever  seen.  We 
see  "empires  rise,  empires  fall,"  apparently  as  the  consequence 
of  such  locational  changes.  We  follow  these  developments  with 
a  strong  feeling  of  their  significance;  we  predict  the  tendencies 
of  future  accumulation  and  distribution,  the  development  of  in- 
dustrial states  and  their  collapse.  We  even  interfere  with  these 
matters  by  our  trade  and  tariff  policies  (Handelspolitik),  and 
try  to  master  them.  In  short,  we  do  repeatedly  a  thousand  things 
which  we  should  really  attempt  only  after  we  have  secured  a 
clear  understanding  of  the  laws  which  operate  within  this  sphere. 
But  can  we  say  that  we  possess  such  a  knowledge?  Can  we  say 
that  in  our  discussions  we  make  use  of  much  more  than  some 
vague  notions  about  the  division  of  labor,  etc.,  while  assuming 
location  to  be  determined  by  the  nature  of  the  particular  proc- 
ess? We  work,  in  spite  of  Thünen  and  his  successors,  almost 
entirely  with  such  tools,  I  believe. 

We  also  notice  enormous  displacements  taking  place  within 
national  boundaries.  We  observe  that  certain  regions  rapidly 
grow  poor  in  human  beings  and  capital,  while  others  become  sat- 
urated. We  see  in  metropolitan  centers  great  masses  conglom- 
erate, seemingly  without  end.  We  philosophize  about  these  mat- 
ters, talk  about  the  advantages  and  disadvantages  which  result, 
about  Asphaltkultur,  or  ''decline  of  morals."  Of  course  we  have 
long  since  become  partisan  in  these  matters.  To  some  of  us  it 
seems  that  the  populace  "runs"  to  the  big  cities  only  for  "pleas- 
ure's" sake — to  the  ultimate  ruin  of  itself  and  its  posterity;  to 
others  it  appears  that  these  people  follow  inevitable  laws,  as  for 
example  the  flow  toward  the  place  of  lowest  pressure  socially, 
etc.  Much  thought  has  been  spent  upon  the  "rush  to  the  city" 
(not  only  upon  its  consequences,  but  also  upon  its  causes),  but 


is  it  possible  for  us  to  arrive  at  any  conclusion  about  its  causes 
when  we  do  not  possess  as  yet  any  real  knowledge  of  the  general 
rules  determining  the  location  of  economic  processes — ^when  the 
purely  economic  laws  which  without  any  doubt  somehow  influ- 
ence location  are  not  discovered? 

Everybody  who  moves  into  a  large  city  goes  there,  among 
other  purposes,  in  order  to  follow  some  economic  pursuit.  Is  it 
sensible  for  us  to  argue  about  cultural  and  social  motives  when 
perchance  we  are  simply  fettered  by  the  iron  chains  of  hard  eco- 
nomic forces?  It  may  be  that  the  enormous  agglomerations  of 
today  are  nothing  but  inevitable  results  of  a  certain  stage  of  eco- 
nomic and  technical  development;  or  perhaps  they  are  the  con- 
sequence of  the  social  organization  of  our  economic  system. 
Concerning  this  we  really  ought  to  have  some  exact  knowledge. 
At  any  rate  we  cannot  very  well  go  ahead  assuming  that  there  are 
no  rules  of  economic  location  at  all,  or  that  people  are  guided  by 
"pleasure"  and  other  irrational  motives  when  choosing  the  loca- 
tion of  their  economic  pursuits,  although  we  know  them  to  be 
controlled  by  hard-and-fast  rules  in  every  other  economic  sit- 

Ambition  might  tempt  us  to  formulate  a  general  theory  of  lo- 
cation. For  it  seems  possible  only  on  the  basis  of  general  rules 
of  locational  distribution  of  economic  forces  to  disclose  the  caus- 
al relation  between  them  and  those  large  displacing  processes 
which  we  observe.  With  such  general  rules  known,  it  would  be 
possible  to  show  how  and  to  what  extent  the  aggregation  of  pop- 
ulation is  determined  by  economic  forces.  Having  acquired  this 
knowledge,  we  might  become  able  to  say  how  far  forces  of  a 
general  cultural  nature  determine  the  location  of  economic  proc- 

But  certain  reasons  make  it  advisable  to  limit  our  inquiry  to 
a  theory  of  industrial  location,  reasons  quite  apart  from  such  en- 
tirely personal  facts  as  the  time  and  strength  of  an  individual. 

For  one  thing,  the  theory  dealing  with  the  nature  of  eco- 


nomic  processes  has,  with  much  profit,  separated  the  spheres  of 
production,  distribution,  and  consumption.  We  gradually  gain 
the  basis  for  a  general  understanding  of  the  economic  system  by 
learning  how  the  phenomena  of  different  spheres  are  interre- 

Still,  as  a  matter  of  fact,  the  locational  forces  operating  be- 
tween the  different  spheres  are  quite  peculiar.  We  may  separate 
production,  distribution,  and  consumption  as  far  as  we  please, 
but,  analyzing  the  locational  character  of  an  economic  system 
(Wirtschaft),  we  need  to  explain  a  large  part  of  each  of  these  at 
the  same  time.  For  example,  the  locational  distribution  of  con- 
sumption appears  to  be,  with  slight  exceptions,  nothing  but  lo- 
cational distribution  within  the  other  two  spheres,  seen  from  a 
different  point  of  view.  Only  the  relatively  inconsiderable  num- 
ber of  people  who  are,  economically  speaking,  merely  consum- 
ers, such  as  officials,  soldiers,  and  persons  of  private  means, 
move  about  independently  of  the  other  two  spheres.  For  the 
rest,  each  producer,  laborer,  merchant,  or  the  like,  wherever  he 
may  be,  affects  to  some  extent  the  location  of  consumption.  In 
turn,  each  consumer,  wherever  he  may  be,  affects  to  some  extent 
the  locational  distribution  within  the  other  two  spheres. 

The  limitation  assigned  to  our  study  is,  therefore,  in  fact,  to 
a  large  extent  a  matter  of  appearance  only.  That  part  of  dis- 
tribution which  represents  the  actual  movement  of  goods  is  ge- 
ographically imbedded  either  between  the  different  parts  of 
production  (productive  process  of  distribution)  or  between  pro- 
duction and  consumption  (consumptive  process  of  distribution). 
It  is  impossible  to  explain  the  sphere  of  production  locationally 
without  including  in  this  explanation  the  distribution  of  mate- 
rial goods  in  all  its  aspects.  In  the  theory  dealing  with  the  nature 
of  economic  processes  it  may  be  possible  to  have  production  end 
at  the  point  where  the  product  is  sold  to  a  merchant,  at  least 
abstractly;  but  for  the  purpose  of  explaining  the  economic  loca- 
tion of  production  this  procedure  is  impossible.  Each  part  of 


production  orients  itself  geographically  with  consumption  in 
mind.  The  explanation  of  this  orientation — locational  theory — 
cannot  neglect  consideration  of  the  place  of  consumption.  Thus 
in  fact  we  include  the  distribution  of  goods  in  our  theory. 

Because  of  this  inevitable  interaction  our  theory  does  not, 
however,  become  a  complete  theory  of  the  location  of  distribu- 
tion. We  in  no  way  explain  thereby  the  location  of  the  seats  of 
the  wholesale  merchants,  of  the  agents  who  direct  the  actual 
movement  of  goods,  i.e.,  the  location  of  the  trading  centers.  The 
headquarters  directing  the  circulation  of  the  goods  and  this  cir- 
culating process  itself  must  be  disconnected  geographically. 

Moreover,  we  say  nothing  definite  regarding  obligations  and 
money,  that  is,  we  say  nothing  definite  concerning  the  location 
of  the  centers  of  capital  and  credit.  This  being  true,  some  as- 
pects of  the  collateral  spheres  of  the  economic  system  remain 
unexplained.  These  collateral  spheres  must  be  treated  separate- 
ly when  one  method  is  that  of  isolating"  the  various  factors. 
And,  for  that  matter,  these  collateral  spheres  have  a  geographi- 
cal movement  of  their  own,  and  their  location  should  according- 
ly be  explained  separately. 

As  has  been  indicated,  if  we  take  the  sphere  of  production 
and  explain  its  location  completely,  we  shall  of  necessity  explain 
also  the  larger  part  of  all  other  locational  problems  within  the 
economic  organism.  Practically  speaking,  we  approach  the  total 
problem  of  economic  location  from  one  particular  point;  the 
first  steps  will  be  a  theory  of  the  location  of  production,  but  the 
last  ones  will  be  essentially  a  general  theory  of  location — or  at 
least  it  will  not  be  very  difficult  to  arrive  at  such  a  theory. 

Limiting  ourselves  thus  to  the  sphere  of  production,  it  is  of 
prime  importance  to  seek  an  explanation  of  the  location  of  in- 
dustrial production.  There  are  good  reasons  why  we  should  con- 
tent ourselves  with  this  analysis.  We  have  a  theory  of  the  loca- 
tion of  agricultural  production  by  Thiinen,  although  it  needs,  I 

^  This  isolating  process,  it  is  true,  is  largely  formal  and  abstract. 


believe,  some  reshaping,  and  particularly  some  developing.  But 
we  do  not  as  yet  have  any  theory  of  the  location  of  industries — 
we  may  say  that  without  doing  injustice  to  the  work  of  Roscher 
and  Schaeffle — although  it  is  obvious  that  industrial  location  is 
far  more  important  for  explaining  the  large  modem  displacing 
processes.  To  be  sure,  very  nice  and  interesting  facts  determine 
the  locational  displacements  of  the  different  methods  of  agricul- 
tural production.  But  they  are  upon  the  whole  simple,  extensive- 
ly analyzed,  well-known  matters,  at  least  to  the  extent  to  which 
they  go  beyond  technical  details  and  influence  international  eco- 
nomic displacements  and  the  modern  aggregations  of  population. 
Moreover,  they  have  in  a  certain  sense  created  only  the  basis  of 
the  general  locational  revolution  of  recent  times;  they  have  pro- 
vided merely  the  groundwork  upon  which  other  forces  have 
arisen  to  displace  economic  processes  and  to  determine  the  ag- 
glomerations of  population.  This  we  sense  quite  distinctly  as 
the  modern  "enigma"  which  is  to  be  solved.  Mysteries  are  not 
contained  in  the  agricultural  sphere.  If  they  can  be  found  any- 
where in  economic  matters,  and  especially  if  they  can  be  found 
in  the  sphere  of  production,  they  will  have  to  be  discovered  in 
the  industrial  sphere  and  in  the  locational  rules  which  control  it. 
The  locations  of  the  industries  form  the  "substance"  (I  do  not 
say  the  cause)  of  the  large  agglomerations  of  people  today.  We 
view  their  movements  quite  superficially,  and  with  perhaps  too 
few  misgivings  as  to  the  international  implications  of  the  shift- 
ing of  forces.  We  argue  seriously  about  tendencies  in  this  sphere. 
It  is  highly  important,  therefore,  to  begin  by  clarifying  these 
tendencies,  not  only  because  they  are  greatly  neglected,  but  also 
because  they  are  most  far  reaching  in  fact. 

How  shall  that  be  done? 

It  is  well  worth  noticing  that  we  know  the  simple  facts  about 
the  distribution  of  agriculture  better  than  those  about  the  dis- 
tribution of  industry.  This  situation  is  quite  easily  explained  by 
the  greater  complexity  of  the  industrial  sphere.  We  have  well- 


developed  statistics  which  cover  fairly  well  the  areas  of  cultiva- 
tion of  the  different  agricultural  products,  the  size  of  the  crops, 
and  their  international  as  well  as  their  local  distribution,  the  lat- 
ter at  least  in  many  countries.  We  have  data,  and  we  can  even 
say  that  on  the  whole  the  data  are  scientifically  analyzed.  The 
essential  aspects  of  agricultural  locational  distribution  and  de- 
velopment are  known  to  us;  if  not,  it  is  our  own  fault. 

With  regard  to  industries,  however,  we  are  confronted  at  the 
very  outset  with  gigantic  difficulties  in  getting  the  mere  mate- 
rial.^ We  do  not  even  know  the  raw  figures  of  international  dis- 
tribution of  production  of  more  than  a  few  trades,  such  as  mines, 
salt  works,  sugar,  tobacco,  and  perhaps  the  mechanical  part  of 
the  textile  industry — in  other  words,  trades  whose  production  is 
analyzed  statistically  for  fiscal  or  other  special  purposes.  For  all 
other  industries  we  use,  for  want  of  better  data,  the  import  and 
export  figures  in  a  manner  scientifically  quite  inadmissible. 
When  we  talk  of  international  distribution  of  industrial  resources 
we  use  figures  which  we  should  not  use  at  all  except  in  terms  of 
their  relation  to  the  size  of  the  original  production.  The  trade 
censuses  which,  by  giving  the  number  of  persons  employed,  give 
us  suggestions  regarding  size,  are  very  difficult  to  compare,  and 
for  that  reason  are  not  thus  used.  This  is  the  situation  regarding 
the  distribution  of  industries  internationally. 

What  is  to  be  said  concerning  the  distribution  within  the  na- 
tional boundaries?  Material  exists  regarding  this,  although  part- 
ly hidden  so  far.  Here  the  trade  censuses,  or  at  least  their  pre- 
liminary and  intermediary  materials,  can  give  us  information 
about  local  displacements  of  a  very  exact  kind  and  free  from  all 
objection.  We  do  not  do  injustice  to  anyone  by  saying  that  this 
really  extensive  material  has  so  far  not  been  analyzed  for  these 
purposes.  The  geographical  conditions  of  distribution  and  local 

^  This  was  written  in  iqog.  But  even  today  many  of  the  essential  facts  are 
not  available. — Editor. 


accumulation  have  nowhere  as  yet  been  analyzed  in  a  careful 
quantitative  way  for  even  one  industry.  Of  what  use  for  our 
purposes  are  beautiful  maps  showing  us  the  regions  within  which 
one  industry  is  practiced  "primarily"  if  we  learn  that  this  same 
industry  is  also  practiced  ''outside"  of  these  regions  within  the 
same  country?*  We  ought  to  know,  for  purposes  of  any  exact 
locational  study,  to  what  extent  they  are  practiced  "inside"  and 
"outside,"  i.e.,  the  relation,  quantitatively  speaking,  between 
the  two.  Similarly  useless  for  our  purpose  are  otherwise  quite 
estimable  maps  which  show  us  the  "relative  geographical  im- 
portance" of  various  industries  in  relation  to  the  population;^ 
they  give  us  information  concerning  the  different  composition  of 
the  population  here  and  there,  but  not  concerning  the  geograph- 
ical distribution  of  the  industry  itself.  If  we  search  for  quanti- 
tatively well  defined  information  regarding  the  local  distribution 
of  industries,  we  soon  find  that  we  grope  in  the  dark  concerning 
all  industries  in  all  countries,  with  perhaps  the  single  exception  of 
mining  and  smelting  production.  We  grope  in  the  dark  concern- 
ing every  single  period  of  the  development  of  a  given  industry 
— and  how  much  more  so  concerning  its  entire  development! 
My  respects,  therefore,  to  economic  treatises  including  any  dis- 
9  cussion  of  local  distribution  of  industry  at  present!  Nothing  is 
to  be  said  against  them  as  things  stand.  We  ought  to  realize, 
however,  that  they  are  in  fact  little  more  than  rather  sketchy 

Obviously  a  change  should  be  brought  about  in  this  situa- 
tion. It  is  necessary  to  canvass  systematically  the  existing  ma- 

*  Compare  the  maps  of  numerous  writings  on  the  English  industries ;  simi- 
larly, the  maps  of  distribution  of  industries  which  are  added  to  the  reports  of 
factory  inspection. 

^  Compare  the  maps  of  the  official  German  reports  on  the  Trade  Census. 
They  are  used  and  even  elaborated  for  the  purpose  of  illustrating  the  location  of 
industry  in  Teubner's  Handbuch  der  Wirtschaftskunde  Deutschlands,  I  suppose 
faute  de  mieux.  For  evidence  that  they  are  not  only  useless  in  principle,  but  that 
one  gets  quite  a  distorted  idea  about  the  whole  matter,  compare  Part  II. 


terial  available  upon  one  period,  and  we  shall  choose  the  German 
development  since  i860  for  that  purpose.  It  is  further  neces- 
sary to  get  a  rehable  picture  by  making  an  exact  quantitative 
analysis  of  the  interrelated  forces  which  affect  the  distribution 
and  agglomeration  of  the  individual  industries.  This  is  the  first 
and  unavoidable  part  of  our  investigation,  to  get  exact  data  re- 
garding the  actual  locational  relations  and  displacements  in  any 
one  tolerably  isolatable  district  for  some  period  of  time,  even  if 
quite  limited.  We  need  to  have  before  us  the  object  with  which 
we  are  dealing,  clear  and  discernible,  and  particularly  measura- 
ble, in  all  its  parts. 

But  we  want  still  more,  and  we  must  attempt  more,  as  has 
been  indicated  earlier.  We  want  to  discover  "laws"  for  the  move- 
ments within  this  (industrial)  body — laws  sufficiently  exact  to 
enable  us  to  measure,  with  their  help,  the  displacement  of  eco- 
nomic forces  in  such  a  way  that  we  can  state  to  what  extent  these 
displacements,  and  to  what  extent  other  factors  cause  the  vast 
geographical  revolutions  of  our  time. 

The  empiricist  will  at  best  look  askance  at  this  larger  and 
more  essential  enterprise.  He  will  in  his  well-known  fashion  tell 
us  that  we  should  have  to  be  able  to  subject  the  social  life  and 
its  forces  to  experiments  if  we  wish  to  find  exact,  i.e.,  scientific, 
laws ;  ^  that  inasmuch  as  we  cannot  do  that,  we  ought  to  content 
ourselves  with  stating  ''probabilities"  and  more  or  less  certain 
''relationships,"  "regularities,"  "phenomena  of  evolution."  Any- 
thing else  is  useless  from  his  point  of  view,  and  we  cannot,  there- 
fore, expect  sympathy  from  that  side.  But  we  may  hope  for 
sympathy  among  those  who  believe  with  us  that  it  is  possible 
without  experiments  to  analyze  further  by  purely  theoretical,  in- 
tensive labor  empirical  evolutionary  phenomena,  in  spite  of  their 
complexity.  By  making  use  of  the  method  of  isolating  analysis, 

®  Scientific  stands  here  for  the  German  term  naturwissenschaftlich,  as  op- 
posed to  geisteswissenschaftlich.  The  distinction  roughly  corresponds  to  "scien- 
tific" and  "philosophic."  Cf.  Rickert,  Kulturwissenschaft  und  Naturwissenschaft, 
4th  ed.,  1 92 1. — Editor. 


we  may  ascertain,  if  not  all,  at  least  some,  causal  relationships, 
and  prepare  for  a  perfect  causal  understanding,  and  even  for 
measurement.  By  the  adherents  of  the  method  of  isolation,  then, 
this  essay,  whether  successful  or  not,  will  probably  be  approved, 
10  at  least  in  principle.  We  hope  that  the  writer,  and  not  the  es- 
say, will  be  blamed  for  its  possible  failure. 

This  will  make  clear  how  we  must  proceed  with  this  essay. 
Obviously,  two  different  purposes  should  be  achieved.  First,  we 
shall  have  to  develop  the  pure  laws  of  industrial  location,  laws 
in  the  strictest  sense  of  the  term  pure,  i.e.,  independent  of  any 
particular  kind  of  economic  system  (Wirtschaftsart)  J  Second- 
ly, we  shall  have  to  show  what  particular  form  these  laws  re- 
ceive in  the  modern  economic  order,  and  what  additional  rules, 
or  perhaps  only  regularities,  enter.  The  second  phase  of  the 
work  will  of  course  contain  an  explanation  of  the  interesting  re- 
lationship^ between  these  two  kinds  of  laws  and  the  large  social 
revolutions  referred  to. 

Methodologically  we  shall  always  proceed  by  isolation,  not 

''  The  concept  of  a  system  of  "pure"  economics  as  indicated  here  occurs  in 
German  theoretical  literature.  It  is  the  outcome  of  an  attempt  to  regain  for  eco- 
nomic theory  a  position  which  it  seemed  to  have  lost  completely  under  the  im- 
pact of  the  historical  school.  Books  like  Karl  Biicher's  Introduction  to  Polit- 
ical Economy  treated  economics  in  terms  of  economic  development.  Usually 
several  stages  were  being  distinguished,  of  which  the  last  is  the  capitalistic  stage, 
or  lately  the  high  capitalistic  (hochkapitalistische  Stufe).  In  order  to  get  a  foot- 
hold outside  this  evolutionary  view  and  to  return  to  theory,  the  expedient  of 
such  an  abstract  "pure"  system  was  used.  It  seemed  sensible  to  say  that  if  all 
these  systems  were  designated  as  economic  systems,  it  was  justifiable  to  search  for 
the  characteristics  which  they  had  in  common,  although  some  will  hold  that  the 
thought  of  the  earlier  thinkers  like  Smith  and  those  following  him  is  "capital- 
istic" and  representative  of  the  stage  of  development  with  which  they  were  con- 
cerned. The  assumption  of  such  a  "pure"  system  of  economics  simply  marks  the 
return  to  what  would  be  styled  "economic  theory"  in  England  and  America.  Cf. 
also  infra,  p.  226,  footnote. — Editor. 

*  Relationship  is  here  used  for  Dynamik,  a  German  word  which  is  not  al- 
ways suited  for  translation  into  the  English  "dynamics,"  and  which  therefore  has 
occasionally  been  rendered  by  "forces"  and  "relationship,"  respectively,  depend- 
ing upon  the  particular  meaning  it  has  in  the  respective  connections. — Editor. 


only  in  the  first  part  dealing  with  the  pure  theory,  but  in  the 
second  part^  as  well.  There  is  one  difference,  however.  For  the 
task  of  stating  the  pure  rules  of  location  it  will  be  possible  to  use 
deduction  exclusively.  We  shall  be  able  to  start  from  certain 
very  simple  premises  and  to  deduce  therefrom  the  entire  system 
(Mechanik)  of  "pure"  rules  of  location.  Naturally,  this  system 
will  apply  only  in  terms  of  these  premises  and  no  further.  It 
will  become  apparent  that  it  is  possible  to  develop  these  pure 
rules  of  location  fully  in  so  far  as  they  are  of  a  general  nature, 
and  apply  therefore  more  or  less  to  all  industries.  For  the  details 
compare  chapter  i. 

The  further  task  of  formulating  the  laws  of  location  under 
modern  capitalism  cannot  be  achieved  by  simple  deduction.  The 
premises  which  determine  the  particular  application  of  the  pure  1 1 
rules  as  well  as  the  additional  rules  governing  reality  are  not 
known  without  further  investigation.  In  order  to  formulate  them 
we  must  first  secure  the  actual  picture  of  industrial  orientation 
(location),  as  it  is  moulded  by  the  modern  economic  life.  Once 
we  have  this  actual  picture  we  shall  have  to  show  to  what  extent 
this  orientation  is  affected  by  unexplained  speciaP^  causes  which 
the  general  theory  has  ignored  and  may  properly  ignore.^^  Fi- 
nally, we  shall  have  to  show  the  effects  of  unexplained  causes  of 
a  general  kind.  For  these  latter  we  shall  have  to  find  the  prem- 
ises which  must  somehow  be  due  to  the  particular  nature  of 
modern  economic  or  social  life.  Only  from  these  premises  may 
we  deduce  the  rules  of  location  "governing  reality,"  which  can 
give  us  a  complete  picture  of  the  distribution  of  locations  and  at 
the  same  time  can  perhaps  give  us  the  means  of  understanding 
the  general  aggregations  of  population  in  modern  times — that  is, 

^  An  outline  of  this  second  part  is  contained  in  Alfred  Weber,  "Industrielle 
Standortslehre  (Allgemeine  und  kapitalistische  Theory  des  Standorts)"  in  Grund- 
riss  der  Sozialökonomik  (1914),  Abteilung  VI,  i,  70-82. — Editor. 

'^^  Due  to  circumstances  in  particular  industries. — Editor. 

"  Details  in  chap.  i. 


so  far  as  such  a  thing  can  be  done  by  an  abstract  theory,  which 
never  explains  entirely  a  concrete  reality. 

Obviously  then,  the  preliminary  canvass  of  facts  which  I 
mentioned  earlier  is  a  necessary  introduction  to  the  later  task  of 
a  '^reahstic"  theory.  I  had,  in  fact,  undertaken  this  preliminary 
work  of  ascertaining  precisely  the  evolution  of  German  indus- 
trial location  since  i860  before  I  had  acquired  any  theoretical 
conception.  I  beheve,  however,  that  it  will  be  better  to  present 
this  factual  material  where  it  belongs,  both  as  a  matter  of  logic 
and  as  a  matter  of  practical  presentation :  after  the  pure  theory 
and  before  the  realistic  theory.  It  is  impossible  to  analyze  or  ar- 
range this  material  at  all  without  an  abstract  theory  of  location. 
I  have  indeed  gained  it  myself  from  this  analysis;  only  out  of  an 
abstract  theory  and  a  clear  survey  of  the  facts  can  the  realistic 
theory  be  compounded.^^ 

We  shall  organize  this  work,  then,  as  follows :  The  first  part 
will  contain  the  pure  theory.  This  is  divided  into  two  parts:  (a) 
the  abstract  disclosure  of  the  economic  forces  which  control  the 
12  orientation  of  industries,  i.e.,  the  analysis  of  the  constituent  ele- 
ments (locational  factors)  determining  the  location  of  industries, 
and  (b)  the  formulation  of  the  laws  according  to  which  these 
factors  work. 

The  second  part  will  contain  the  ''realistic"  theory  and  will 
be  based  upon: 

a)  An  analysis  of  the  locational  distribution  (Lagerung)  of 
German  industries  since  i860. 

b)  An  analysis  of  some  other  data  which  are  available  con- 
cerning the  aggregation  of  population  in  modern  capitalistic 

We  shall  see  that  the  kind  of  industrial  location  which  we 
have  today  is  not  entirely  explained  by  the  "pure"  rules  of  loca- 

"  It  has  to  be  kept  in  mind  that  Professor  Weber  does  not  work  out  his  so- 
called  "realistic"  theory  in  this  volume.  An  approach  to  it  is  made  in  his  con- 
tribution to  the  Grundriss  der  Sozialökonomik. — Editor. 


tion,  and  therefore  is  not  purely  "economic."  It  results  to  a  large 
extent  rather  from  very  definite  central  aspects  of  modern  cap- 
italism and  is  a  function  of  modern  capitalism  which  might  dis- 
appear with  it.  It  results,  we  may  say  in  hinting  at  the  main 
point,  from  degrading  labor  to  a  commodity  bought  today  and 
sold  tomorrow,  and  from  the  ensuing  laws  determining  the  labor 
market  {Gesetze  der  " Arbeitsmarktgestaltung^')  and  from  the 
local  "agglomeration  of  workers"  created  thereby.  This  agglom- 
eration of  workers  produces  by  necessity  the  particular  kind  of 
industrial  aggregations  which  we  find  today  and  which  I  shall 
call  "progressive  agglomeration  of  industry"  {Stufenagglomera- 
tion der  Industrie) .  Therefrom  results,  as  we  shall  have  to  show, 
the  phenomenon  of  modern  aggregations  of  population  and,  of 
course,  many  other  things. 

I  say  this  only  to  indicate  that  the  "realistic"  theory  will  en- 
able us  to  arrive  at  certain  fairly  general  conclusions  which 
explain  at  least  a  part  of  the  dynamics  of  the  large  modern  geo- 
graphical revolution.  But  only  a  part;  the  limit  of  the  conclu- 
sions of  the  second  section  of  our  study  will  be  found  in  the  limits 
of  its  material.  This  material  deals  mainly  with  the  movements 
of  industry  within  only  a  part  of  the  international  economic  or- 
ganism— within  a  territory  which  represents  a  politically,  and, 
generally  speaking,  a  nationally  uniform  organization.  This  lim- 
itation in  the  material  has  the  advantage  that  the  movements 
of  industry  thus  studied  present  themselves  to  the  observer  as,  in 
a  sense,  "pure."  They  take  place  without  regard,  on  the  one  13 
hand,  to  any  differences  of  political  organization  and  to  the  in- 
fluence of  trade  and  tariff  policies;  and  without  regard,  on  the 
other  hand,  to  differences  of  race,  climate,  and  environment.  Our 
studies  thus  provide  without  doubt  an  analysis  for  one  country, 
and  apparently  they  provide  the  first  necessary  step  toward  a 
similar  theory  for  the  Weltwirtschaft  (economic  system  of  the 
world) ;  for  a  general  theory  would,  at  the  outset,  also  disregard 
the  constituent  differential  elements  just  mentioned  and  would 


introduce  them  afterward/^  The  limitation  in  the  material  has, 
however,  a  disadvantage  in  that  it  does  not  help  us  to  ascertain 
precisely  the  significance  of  each  of  the  differentiating  factors 
mentioned  above.  In  this  respect  the  limitations  of  the  material 
set  a  limit  to  everything  attempted  in  this  essay,  a  fact  which 
cannot  be  emphasized  strongly  enough. 

This  is,  of  course,  the  point  at  which  further  study  is  desir- 
able. It  should  be  said,  however,  that  further  research  becomes 
rather  difficult.  We  need,  in  order  to  get  ahead,  rather  diversi- 
fied new  data.  We  need  primarily  clarity  as  to  ideas  and  facts 
concerning  the  general  significance  of  such  fundamental  factors 
as  national  disposition  (Volksanlage)  and  environment — both 
their  general  significance  and  their  relationship  to  what  we  call 
labor  supply  (Arbeiterstamm).  We  need  to  ascertain  precisely 
how  far  the  quality  in  its  different  parts  of  industrial  output  de- 
pends upon  the  "stock  of  industrial  workers"  in  different  cli- 
mates (Zonen)  and  among  different  nations,  and  how  far  this 
dependence  changes  within  the  framework  of  the  modern  tech- 
14  nical  and  economic  development,  etc.^*  For  an  understanding  of 
the  international  problem  we  need,  moreover,  investigations  into 
the  actual  effects  of  political  interferences  (such  as  trade  poHcies 
and  labor  policies)  upon  the  local  grouping  of  economic  forces-^ 
studies  which  we  do  not  possess  at  present  in  spite  of  all  our  the- 
orizing regarding  international  trade  and  tariff  policies.    We 

^"  There  is  no  question  that  the  importance  of  some  of  these  differentiating 
factors  (particularly  the  trade  and  tariff  policy)  is  generally  very  much  over- 
estimated today.  But  there  is  no  question,  either,  that  others,  like  climate  and 
cultural  environment,  perhaps  even  "race,"  have  considerable  importance — so 
considerable,  in  fact,  that  they  will  be  felt  even  in  analyzing  the  seemingly  uni- 
form German  body,  and  that  some  "dark  spots"  which  remain  can  hardly  be  ex- 
plained except  by  them.  The  available  statistical  material  unfortunately  does  not 
allow  to  solve  these  problems. 

'*  Cf .  in  this  connection  the  researches  of  American  sociologists,  i.e.,  Clark 
Wissler,  Man  and  Culture,  F.  Stuart  Chapin,  Cultural  Changes,  and  P.  Sorokin. 
Social  Mobility. — Editor. 


should  also  secure  an  enormous  mass  of  material  concerning  the 
international  distribution  of  industrial  location  {internationale 
Industrielagerung),  etc.  These  are  many  and  difficult  matters. 

But  irrespective  of  this,  we  shall  of  course  find  that  much  of 
what  is  presented  within  the  narrow  frame  of  this  essay  must  be 
corrected,  and  the  reader  will  observe  that  there  remain  unsolved 
problems,  a  fact  which  will  not  be  concealed. 

This  book  is  expected  to  be  a  beginning,  not  an  end.  15 



The  economic  causes  determining  the  location  of  an  industry 
seem  to  be  a  network  of  complex,  diverse  elements,  often  in  in- 
dividual instances  so  arbitrarily,  or  at  least  incidentally,  com- 
posed that  there  appears  to  be  no  place  for  more  than  an  analysis 
of  the  individual  case/  It  seems  impossible  to  make  any  general 
statement  for  most  industries  concerning  the  places  to  which 
their  factories  must  go  or  concerning  the  causes  upon  which 
their  locations  depend.  If  we  approach  the  individual  manu- 
facturer with  a  question  concerning  the  choice  of  his  location,  he 
will  at  most  give  us  a  quaint  concoction  of  general  and  particular 
reasons,  unless  he  points  to  the  past  and  says:  ''I  am  here  be- 
cause this  industry  grew  up  here."  This  concoction  will  be  dif- 
ferent for  each  factory  and  will  present  whatever  general  causes 
it  contains  in  a  particular  individual  setting.  Thus  one  might 
well  despair,  as  I  have  said,  of  discovering  general  formulas  for 
the  solution  of  the  different  elements,  or  even  of  ascertaining  pre- 
cisely their  limits.  Still,  an  attempt  to  do  so  is  quite  necessary 
from  a  theoretical  point  of  view.  However  difficult  it  seems,  we 
must  try  to  disentangle  the  knot  of  causes  which  confronts  us 
everywhere  in  reality,  and  to  isolate  and  group  the  elements  com- 
posing it. 


In  order  to  do  this  we  need  a  clear  understanding  of  two 
terms:  first,  the  forces  which  operate  as  economic  causes  of  lo- 

'  Cf.  R.  M.  Haig,  "Some  Aspects  of  the  Regional  Plan  of  New  York  and  Its 
Environs,"  and  "Toward  an  Understanding  of  the  Metropolis,"  Quarterly  Jour- 
nal of  Economics,  Vol.  XL. — Editor. 



1 6  cation,  the  ''locational  factors";  and  second,  the  objects  which 
we  believe  those  causes  to  act  upon,  the  ''locational  units." 

By  "locational  factor"  we  mean  an  advantage  which  is 
gained  when  an  economic  activity  takes  place  at  a  particular 
point  or  at  several  such  points  rather  than  elsewhere.  An  ad- 
vantage is  a  saving  of  cost,  i.e.,  a  possibility  for  the  industry  to 
produce  at  this  point  a  certain  product  at  less  cost  than  else- 
where, to  accomplish  the  entire  productive  and  distributive  proc- 
ess of  a  certain  industrial  product  cheaper  at  one  place  than  at 

We  say  the  productive  and  distributive  process  of  a  certain 
product.  We  shall  always  compare  for  one  and  the  same  product 
the  advantages  of  production  as  represented  by  locational  fac- 
tors; since  only  the  production  of  one  and  the  same  product 
constitutes  a  unit  with  regard  to  the  spatial  distribution  of  which 
we  may  speak  with  sufficient  accuracy. 

It  is  necessary  to  be  exact  in  this  respect:  a  given  com- 
modity of  better  quality  is  not  the  same  product  as  the  same 
commodity  of  inferior  quality,  at  least  not  in  principle.  The  pro- 
duction of  each  is,  from  a  theoretical  point  of  view,  a  "unit"  in 
itself  which  is  distributed  over  an  area  according  to  its  pecu- 
liarities. These  units  can  and  do  compete  with  each  other;  the 
better  commodity  may  supplant  the  less  good,  or  vice  versa,  and 
this  may  also  affect  their  locations  eventually.  But  this  competi- 
tion or  displacement  is  not  essentially  a  locational  struggle ;  it  is 
based  upon  competitive  causes  of  a  different  kind.  It  does  not 
concern  us  for  the  moment.  It  represents  the  displacement  of 
one  industry  by  another,  in  the  same  way  in  which  wood  and  clay 
products  are  superseded  by  iron  goods.  It  is,  however,  an  object 
of  our  study  to  learn  whither  the  victorious  or  the  defeated  in- 
dustry and  the  production  of  the  different  qualities  move.  We 
have  to  solve  that  problem  by  analyzing  the  local  distribution  of 
the  productive  advantages  which  are  decisive  for  this  particular 

17  quality,  this  "locational  unit." 


It  is  obvious  that,  practically  speaking,  it  may  and  fre- 
quently will  be  the  case  that  the  extent  and  the  importance  of 
a  given  productive  advantage  is  negligible  as  between  different 
j  qualities  of  the  same  product.  It  may  happen  that  for  different 
qualities  of  a  product  the  locational  factors  are  so  similar  that 
they  are,  practically  speaking,  equal.  But  even  so,  these  different 
qualities  represent  independent  units  for  the  purpose  of  loca- 
tional analysis.  It  must  be  kept  in  mind  that  each  of  the  qualities 
has  its  particular  sphere  of  consumption,  competing,  perhaps, 
but  separate.  It  is  consequently  not  possible  to  treat  the  produc- 
tions of  these  different  qualities  as  one  locational  unit,  even 
I  though  they  are  in  close  proximity  (have  deposits  of  raw  ma- 
i  terials  and  other  real  locational  elements  in  common).  We  have 
i  to  deal  with  two  different  productions  which  happen  to  find  their 
locations  according  to  similar  causes. 

The  foregoing,  however,  is  the  abstract  position  of  pure  the- 
ory. As  a  matter  of  fact,  there  is  in  reality  an  enormously  wide 
field  in  which  the  competition  of  quality  changes  to  that  of  price, 
and  in  which  products  of  a  different  but  closely  approximate 
quality  are  in  fact  treated  as  one  and  the  same  product  at  dif- 
ferent prices.  Viewing  the  matter  closely,  one  is  compelled  to 
admit  that  each  "competition  of  price"  rests  partly  upon  such  a 
difference  in  quality;  because  the  quality  of  no  product  is  truly 
equal  to  that  of  any  other.  Competition  of  price  is  possible  only 
by  disregarding  differences  of  quality. 

Still,  whenever  in  reality  no  difference  of  quality  is  recog- 
nized, we  do  not  need  to  recognize  it  when  applying  theory  to 
reality.  In  such  a  case  we  have  before  us,  for  this  one  application 
at  least,  "units"  of  location  of  production.  The  different  qualities 
of  product  have  been  welded  together  into  a  unit  by  life  through  18 
being  treated  as  one  by  consumption.  Accordingly,  we  shall 
treat  as  locational  units  varied  products  whose  distribution  of 
production  over  an  area  is  properly  to  be  analyzed  as  a  unit. 


This  much  regarding  the  nature  of  the  terms,  locational  fac- 
tors and  locational  units. 


How  shall  we  group  these  locational  factors?  We  seek  a 
general  theory  of  location;  that  is  to  say,  we  wish  to  resolve  the 
seeming  chaos  of  the  local  distribution  of  production  into  the- 
oretically general  rules.  Such  general  rules  would  result  only 
from  the  operation  of  locational  factors  of  a  general  nature,  if  at 
all.  Such  general  locational  factors  must  be  considered  for  every 
industry,  asking  in  the  case  of  each  industry  in  what  way  they 
exercise  their  general  influence  and  to  what  extent.  Thus  the 
first  question  is:  Are  there  such  general  causes  of  location  which 
concern  every  industry?  And  the  next  question  is:  Are  there 
any  special  causes  of  orientation  which  concern  only  this  or  that 
industry,  or  this  or  that  group  of  industries?  Such  special  causes 
obviously  are  the  result  of  the  peculiar  technical  or  other  nature 
of  an  industry  or  group  of  industries.  How  far  can  the  location 
of  industries  be  explained  by  general  causes,  and  how  far  only  by 
introducing  special  causes?  It  is  obviously  helpful  to  classify 
locational  factors  as  general  and  special.  It  may  elucidate  the 
difference  to  state  at  this  point  that  the  cost  of  transportation,  of 
labor,  and  rent  are  general  factors,  since  they  should  be  consid- 
ered in  the  case  of  every  industry,  influencing  it  ''more  or  less  in 
19  one  way  or  in  another."  On  the  other  hand,  the  perishability  of 
raw  materials,  the  influence  of  the  degree  of  humidity  of  the  air 
upon  the  manufacturing  process,  the  dependence  upon  fresh 
water,  etc.,  are  special  locational  factors,  because  they  concern 
particular  industries  only. 

All  locational  factors,  whether  general  or  special,  are  to  be 
further  classified  according  to  the  influence  which  they  exercise 
(i)  into  such  as  distribute  the  industries  regionally  and  (2)  into 
such  as  ''agglomerate"  or  "deglomerate"  industries  within  the 
regional  distribution.  To  "distribute  regionally"  means  to  direct 


industry  toward  places  on  the  surface  of  the  earth  which  are 
geographically  determined  and  given,  to  draw  industry  to  definite 
regions  and  thus  to  create  a  fundamental  framework  of  indus- 
trial locations.  To  "agglomerate"  and  to  ''deglomerate"  means 
to  contract  industry  at  certain  points  within  such  a  framework 
(irrespective  of  where  the  framework  may  be  situated  geograph- 
ically), and  thus  to  determine  the  agglomerations  which  industry 
shows  within  the  framework — something  quite  distinct  from  the 
process  of  regional  distribution. 

If  industry  is  influenced  by  the  cost  of  transportation  or  by 
geographical  differences  in  the  cost  of  labor,  industry  is  drawn  to 
points  geographically  quite  definite,  though  changing  their  posi- 
tion as  industry  develops.  The  factors  which  operate  thus  are 
regional  factors  of  location.  If  industry,  however,  is  brought  to- 
gether at  certain  points  by  price  reductions  due  to  agglomeration 
itself,  whether  it  be  the  more  economical  use  of  machinery  or 
merely  the  advantage  of  being  at  a  place  where  auxiliary  trades 
are  located;  or  if  industry  is  driven  from  such  congested  places 
by  the  high  rent;  industry  is  agglomerated  or  spread  within  its 
geographical  network  according  to  certain  general  rules  which 
are  quite  independent  of  geography.  The  factors  which  operate 
thus  are  agglomerative  or  deglomerative  factors. 

A  third  distinction  which  ought  to  be  made  is  that  of  natural 
and  technical  factors  on  the  one  hand  and  of  social  and  cultural 
factors  on  the  other  hand.  This  distinction  (also  made  in  terms  20 
of  the  effects  of  the  factors)  cannot  be  fully  made,  however,  for 
reasons  to  be  considered  shortly.  It  has  the  following  meaning: 
The  advantages  which  draw  industries  hither  and  thither  may 
be  given  by  nature.  In  that  case  they  could  be  altered  only  by 
changes  of  these  natural  conditions,  by  the  extent  of  the  control 
of  nature — in  other  words,  by  technical  progress.  They  would 
be  independent  of  the  particular  social  and  cultural  circum- 
stances; at  least  there  woud  be  no  direct  dependence.  On  the 
other  hand,  the  advantages  which  draw  industries  hither  and 


thither  may  be  social  or  cultural  phenomena,  the  consequence  of 
particular  economic  or  social  conditions,  or  of  a  certain  civili- 

For  example,  all  differences  in  cost  which  result  from  the 
spatial  position  and  climate  of  different  places,  particularly  all 
differences  of  cost  of  transportation,  are  locational  factors  of  the 
natural  and  technical  kind,  phenomena  of  nature  which  may 
only  be  altered  by  the  technical  evolution.  The  differences  of  the 
cost  of  some  types  of  labor  may  be  of  the  same  nature  (differ- 
ences in  the  hereditary  qualities  of  the  population),  or  they  may 
be  the  result  of  a  certain  cultural  environment  (differences  in 
the  standard  of  living,  or  in  acquired  productivity  of  labor),  and 
they  are  sometimes  locational  factors  of  a  mixed  kind.  If  a  dif- 
ferent interest  rate  prevails  at  different  locations  of  industry, 
that  is  something  which  bears  no  relation  to  any  natural  condi- 
tion, and  represents  a  purely  ''social"  factor  of  location. 

It  is  desirable  to  make  a  clear  distinction  between  natural 
and  social  locational  factors.  Under  our  method  of  procedure 
this  distinction  is  bound  to  have  considerable  significance  for  us 
later.  For  it  is  apparent  that  every  aspect  of  locational  factors 
which  is  not  of  a  natural  or  technical,  but  of  a  social,  character 
cannot  be  an  object  of  pure  theory  which  is  to  be  independent  of 
particular  economic  or  social  conditions.  Such  aspects  must  be 
left  to  empirical  theory.  The  importance  of  this  classification  of 
locational  factors  is  indicated  by  the  fact  that  it  defines  the  two 
21  large  subdivisions  of  our  theoretical  analysis. 

But  it  will  prove  its  value  later.  For  the  present  we  shall  at- 
tempt to  build  up  the  "pure"  theory  without  applying  the  dis- 
tinction fully  or  exactly.  To  be  specific,  we  shall  exclude  from 
the  purview  of  the  pure  theory  all  locational  factors  of  a  purely 
social  and  cultural  nature  which  our  analysis  of  reality  reveals. 
We  shall  not  even  investigate  how  far  the  natural  and  technical 
factors  contain  in  their  present  form  social  and  cultural  elements 
which  are  due  to  the  particular  economic  and  social  order,  the 


particular  civilization  of  today.  In  order  to  be  exact  we  ought 
to  make  this  investigation  and  then  apply  these  social  and  cul- 
tural elements  in  the  empirical  or  realistic  theory.  But  this  will 
not  be  done.  It  will  appear  that  these  elements  do  not  alter  fun- 
damentally the  laws  according  to  which  they  work;  they  merely 
determine  in  particular  how  these  laws  work  out  in  reality.  It 
is  better  to  state  at  once  these  particular  qualifications  of  the 
general  rules,  and  to  do  so  within  the  framework  of  the  discus- 
sions of  the  pure  theory,  then  to  leave  them  to  a  special  treat- 
ment. Accordingly,  the  analysis  of  the  pure  theory  will,  upon 
the  basis  of  the  natural  and  technical  factors,  be  carried  into  the 
ramifications  which  the  modern  economic  order  presents.  This 
method  of  treatment  will  enable  us  to  reach  the  problem  of 
reality  at  our  first  attempt,  and  at  the  same  time  to  verify  prin- 
ciples by  reference  to  actual  life.  2  2 

Our  analysis  will  be  based  upon  the  distinction  between  gen- 
eral and  special  factors  of  location  and  upon  the  distinction  be- 
tween regional  and  agglomerative  factors.  The  distinction  be- 
tween natural  and  social  factors  will  only  silently  accompany 
our  discussion. 


Can  we  survey  the  several  individual  locational  factors 
which  are  to  be  found  in  the  various  industries?  Obviously,  a 
complete  survey  could  be  made  only  empirically.  There  is  no 
method  by  which  one  could  deduce  from  known  premises  the 
special  locational  factors  which  exist  for  given  industries  on  ac- 
count of  natural  or  technical  peculiarities.  But,  after  all,  this  is 
not  what  we  need  in  order  to  group  the  chaos  of  facts  conven- 
iently for  analysis  and  theory.  We  need  a  knowledge  of  the  gen- 
eral factors  of  location  which  are  applicable  to  a  greater  or  lesser 
degree  in  every  industry.  If  we  know  these  we  are  able  to  inquire 
how  far  the  orientation  of  industries  can  be  explained  by  them. 
Next,  1-  y  ascertaining  further  facts,  we  can  investigate  the  par- 


ticular  causes  of  phenomena  not  explained  by  the  general  fac- 
tors. These  causes  must  spring  from  the  specific  characteristics 
of  particular  industries;  they  are  particular  locational  factors 
which  we  do  not  recognize  in  advance,  and  can  ascertain  only  by 
investigation.  We  shall  attempt  only  the  development  of  a  the- 
ory which  explains  the  working  of  the  general  factors.  This 
theory  can  be  developed  after  a  survey  of  the  general  factors  has 
provided  its  basis. 

We  can  further  limit  ourselves  with  respect  to  the  locational 
factors  needed  as  a  basis  for  our  pure  theory  by  considering  only 
general  factors  of  the  regional  type.  If  we  know  these  and  their 
working,  we  can  abstractly  construe  the  geographical  frame- 
23  work  which  is  created  by  them  (cf .  above) .  We  can  put  in  as  one 
single  force  all  the  agglomerative  and  deglomerative  factors  and 
general  causes  of  orientation  not  yet  analyzed.  They  tend  to 
create  a  certain  number  of  agglomerations  of  a  certain  size — 
agglomerations  which  are  not  due  to  geographical  influences. 
This  single  force  may  easily  be  imagined  to  be  the  resulting  force 
which  is  invariably  derived  from  the  counteraction  of  agglomera- 
tive and  deglomerative  factors.  We  need  only  to  analyze  the 
importance  and  the  working  of  this  resulting  force.  The  factors 
composing  it  we  do  not  need  to  know.^  In  short,  the  pure  theory 
may  be  based  solely  on  the  knowledge  of  the  general,  regional 
factors  of  location  which  control  industry. 

We  have  a  simple  method  of  ascertaining  them.  We  can 
find  all  general  factors  of  location  controlling  industry  (with 
the  exception  of  the  agglomerative  and  deglomerative  factors) 
by  analyzing  some  isolated  process  of  production  and  distribu- 
tion. These  general  factors  must  be  at  work  in  any  such  process, 
and  may  therefore  be  discovered  by  analyzing  it.  The  agglomer- 
ative factors  are  excepted  because  they  are  at  work  between 
industries,  and  therefore  cannot  be  found  in  an  isolated  process. 

^More  regarding  this  point  in  the  chapter  on  ''agglomeration,"  below. 


But  we  are  not  looking  for  them,  an5rway;  we  are  looking  for  the  24 
regional  factors,  and  they  may  be  found  in  the  way  indicated. 

We  have  to  find,  obviously,  those  elements  of  cost  which 
differ  according  to  the  location  of  the  productive  process.  If  we 
can  secure  them,  we  have  the  regional  factors  of  location  of  a 
general  nature.  "Locational  factors"  are,  according  to  our  defini- 
tion, "advantages  in  cost."  They  depend  upon  the  place  to  which 
industry  goes,  and  therefore  pull  industry  hither  and  thither. 
This  idea  is  decisive  for  our  entire  further  procedure. 

Abstractly  considered,  an  industrial  process  of  production 
and  distribution  contains  about  the  following  steps  or  stages: 
(i)  securing  the  place  (real  estate  or  ground  site)  of  the  location 
and  the  fixed  capitaP  for  equipment;  (2)  securing  the  materials 
(raw  and  auxiliary  materials  as  well  as  half -finished  products), 
and  the  power  and  fuel  materials,  (coal,  wood,  etc.);  (3)  the 
manufacturing  process  itself;  (4)  the  shipping  of  the  goods.  In 
each  of  these  steps  a  certain  expenditure  of  natural  resources 
and  labor  is  invested.  In  some  cases  this  expenditure  has  already 
been  taken  care  of  to  a  greater  or  less  degree,  as  in  the  case  i  or 

2  of  fixed  capital  or  half -finished  products.  In  other  cases,  as  in 

3  and  4,  it  falls  entirely  within  the  stage  of  production  which  is 
under  observation.  Each  of  these  expenditures  precipitates  itself  25 
into  the  price  (Warengeldpreis)  which  is  secured  for  the  product 

on  the  market.  The  expenditures  of  3  and  4  are  primarily  labor 
costs;  those  of  i  and  2,  primarily  material  costs.  In  analyzing 
the  price  of  industrial  products  we  meet  again  in  the  guise  of 
monetary  elements  all  those  elements  of  cost  which  grow  out  of 
the  expenditure  of  goods  and  labor  in  the  productive  process. 
We  have  to  ascertain,  first,  which  of  these  monetary  elements 
(in  so  far  as  they  are  elements  of  cost)  differ  according  to  the 
location  of  the  particular  industry.  These  are  the  general  re- 
gional factors  of  location.  We  have  to  discover,  second,  which 

^  For  this  use,  cf .  Palgrave,  Dictionary  of  Political  Economy,  article  on 
"Capital." — Editor. 


of  them  are  expressions  of  a  particular  economic  order  {Wirt- 
schaftsform) and  which  are  expressions  of  every  economic  sys- 
tem. The  latter  will  be  the  general  regional  factors  of  industrial 
production,  even  though  they  appear  in  the  forms  of  the  modern 
capitahstic  order. 

We  shall  have  to  base  our  theory  upon  these  factors  in  their 
modem  capitalistic  form,  which  is  the  only  one  practically  avail- 
able for  analysis.  Nevertheless  we  work  with  the  elements  of 
the  abstract  economic  order  {reine  Wirtschaft)  and  accordingly 
formulate  a  cheory  which  applies  to  this  abstract  order  also. 

The  following  remarks  should  be  made  concerning  the  fore- 
going analysis  of  the  "natural"  industrial  process  as  transformed 
by  the  capitalistic  economic  order.  All  expenditures  of  labor  and 
goods  which  constitute  the  process  become  monetary  advance 
payments  upon  the  future  price  of  the  product.  By  monetary 
advance  payments  we  mean  that  the  entrepreneur  of  each  state 
of  production  makes  advance  payments  in  the  form  of  wages 
and  salaries  to  his  employees,  and  in  the  form  of  prices  paid  for 
materials  and  machines  to  the  entrepreneurs  of  the  previous 
stage.  The  monetary  outlays  of  a  certain  stage  of  production  are 
nothing  but  the  sum  of  all  these  advances  which  its  entrepre- 
neurs must  make.  It  should  be  remarked,  however,  that  each 
26  stage  adds  two  things  to  its  advance  payments:  the  interest  on 
the  capital  it  uses  for  these  advances,  and  its  "profit."  In  each 
successive  stage  these  "additions"  appear  as  increases  of  the 
cost  of  materials.  Thus  the  monetary  costs  are  advance  pay- 
ments covering  not  only  expenditure  of  goods  and  labor  but  also 
of  interest  and  profit  of  the  preliminary  stages  as  well.  These 
remarks  may  suffice  to  clarify  the  nature  of  the  process  which 
we  are  about  to  analyze.  What  form  does  this  process  take  if 
observed  in  connection  with  the  "natural  organization"  of  a  stage 
of  production  as  shown  previously? 

I.  The  first  step  in  the  natural  process  of  production  was 
the  securing  of  the  real  estate  for  the  location,  and  the  securing 


of  the  fixed  capital.  This  becomes  cost  of  rent  so  far  as  the  secur- 
ing of  real  estate  is  concerned,  and  cost  of  money  [interest  plus 
brokerage  charges  plus  taxes — Ed.]  so  far  as  the  securing  of  fixed 
capital  is  concerned. 

The  real  estate  is  not  consumed;  the  fixed  capital  is  con- 
sumed but  gradually.  Both  appear  in  the  final  price  of  the  prod- 
uct as  the  interest  rate  of  the  sums  spent  on  them.*  In  addition, 
the  fixed  capital  appears  with  a  monetary  rate  of  amortization 
proportionate  to  the  time  required  to  consume  the  fixed  capital. 

2.  The  securing  of  the  materials  and  power  which  consti- 
tutes the  second  step  in  the  "natural"  process  of  production  is 
divided  into  the  monetary  cost^  at  the  place  of  their  production 
and  the  cost  of  transporting  them^  to  the  place  of  their  consump- 
tion. We  shall  not  analyze  the  costs  of  transportation  for  the 
present.  The  total  price  (Anschaffungspreis)  paid  for  the  ma- 
terials and  power  supplies  plus  the  interest  resulting  from  the 
advance  of  funds  used  for  buying  them  enters  the  market  price 
(Warenpreis) ;  so  do  the  costs  of  transportation. 

3.  The  third  step,  the  process  of  transforming  the  materials, 
entails  the  consumption  of  the  materials,  the  depreciation  (Ab- 
nutzung) of  fixed  capital  (Stehendes  Kapital)  and  the  utilization 
of  human  labor.  The  first  two  elements  of  cost  have  been  con- 
sidered already.  The  last  one  enters  into  the  market  price  (Wa- 

*  It  is,  of  course,  of  no  significance  whether  this  capital  enters  into  the  proc- 
ess as  loans,  so  that  the  interest  rate  is  stated  by  contract,  or  as  the  entrepre- 
neur's own  capital.  It  must  always  be  there,  it  is  always  consumed,  and  its  in- 
terest rate  must  be  provided  for.  The  stipulated  interest  rate  is,  as  is  well  known 
to  theory,  nothing  but  the  expression  of  the  interest  on  capital,  becoming  ap- 
parent under  certain  circumstances.  Resting  in  principle  upon  Böhm-Bawerk, 
although  in  a  somewhat  more  narrow  sense,  it  is  important  for  the  analysis  of 
cost  as  given  here  that  I  interpret  this  general  interest  on  capital  (Kapitalzins) 
as  the  price  paid  for  goods  enabUng  one  to  overcome  time  (Zeitüberwindungs- 
güter). This  advanced  capital  (Vorschusskapital),  then,  makes  possible  all  the 
advance  payments  which  compose  the  monetary  costs  as  explained. 

°  I.e.,  the  price  to  be  paid  for  them. — Editor. 

®  I.e.,  the  price  to  be  paid  for  transporting  them. — Editor. 


renpreis)  as  wages;  but  again,  of  course,  plus  the  interest  on  the 
advance  of  funds  involved. 

4.  The  fourth  step,  the  shipping,  is  represented  by  the 
costs  of  transportation  which  further  increase  the  price  by  their 
full  amount  plus  the  interest  on  the  funds  used. 

It  should  be  noted  here  that  in  all  these  stages  an  additional 
element  of  cost  exists  which  is  called  today  general  expenses, 
i.e.,  expenses  of  the  general  management,  taxes,  insurance,  etc. 

If  we  group  all  these  elements  of  cost  according  to  their 
character  and  if  we  add  as  the  last  element  of  the  price  the  profit 
of  the  entrepreneur,  we  get  the  following  elements  composing 
the  price  (Warenpreis):  (i)  Profit.  (2)  The  interest  rates  of 
the  fixed  and  operating  capital  {Anlage  und  Betriebskapital)  of 
the  different  stages.  (3)  The  rate  of  amortization  of  the  fixed 
capital.  (4)  The  cost  of  securing  materials  and  power.  (5)  The 
wages.  (6)  The  cost  of  transporting:  {a)  the  (raw)  materials 
28  and  power,  {b)  the  finished  products.  (7)  The  general  expenses. 

Of  these  we  can  eliminate  two,  namely,  i  and  7,  from  fur- 
ther consideration.  Let  us  take  up  first  the  general  expenses  ( 7) . 
To  the  extent  that  they  are  artificial  enhancements  of  the  ex- 
pense of  production  by  political  or  other  agencies  (taxes,  insur- 
ance), they  do  not  belong  in  the  field  of  ''pure"  theory.  To  the 
extent  that  they  are  "natural"  costs  (general  management, 
etc.),  the  local  differences  determined  by  geographical  condi- 
tions which  might  make  them  regional  factors  of  location  are  not 
sufficient  to  make  them  worthy  of  consideration  in  the  general 

As  for  profits  (i),  they  can  never  (at  least  not  in  the  last 
stage  of  industrial  production)  become  locational  factors  be- 
cause they  are  not  elements  of  price,  but  its  result.  They  can 
become  an  element  of  cost  only  by  entering  into  the  cost  of  ma- 
terials, etc.,  of  succeeding  stages  as  profits^  of  earlier  stages.  As 

^It  has  often  been  observed  that  English  poHtical  economy  has  not  sepa- 
rated profit  from  interest  and  wages  of  management.  But  Weber  separates  them 


such  an  element  of  cost  they  may  become  a  locational  factor  for 
the  later  stages  because  it  is  conceivable  that  profits  will  vary 
from  region  to  region  and  thus  affect  the  ''natural"  price  of  se- 
curing the  materials  (cf.  Böhm-Bawerk).  To  give  an  illustra- 
tion: If  a  coal-trading  association  today  fixes  prices  which  vary 
from  district  to  district  and,  not  contenting  itself  with  the  same 
profits  in  all  districts,  collects  higher  profits  in  a  "safe"  district 
by  manipulating  {Normierung)  the  price,  then  local  differences 
of  profits  will  become  regional  factors  of  location  for  all  stages 
of  industrial  production  using  coal.  Thus,  differences  of  profit 
may  become  locational  factors.  Nevertheless  we  can  eliminate 
the  varying  rate  of  profit  from  consideration,  for  it  is,  like  profit 
itself,  not  an  element  of  the  ''pure"  economic  order,  but  rather 
one  of  the  capitalistic  order.  It  does  not  concern  us  in  pure  the-  29 
ory.  It  is  one  of  the  alterations  which  the  capitalistic  order  pro- 
duces in  the  pure  order. 

The  remaining  elements  of  price  (2-6)  which  are  relevant 
for  pure  theory  we  may  group  more  simply,  i.e.,  more  in  accord- 
ance with  the  "natural"  process  of  production.  The  second  ele- 
ment, the  interest  rate  on  the  capital  employed,  depends  appar- 
ently upon  two  factors,  the  interest  rate  and  the  amount  of 
capital.  The  amount  of  capital  employed  is  apparently  deter- 
mined by  the  prices  of  the  various  other  elements  of  production 
(real  estate,  fixed  capital  (Stehende  Sachkapitalien) ,  materials, 
wages,  transportation  rates).  From  this  it  follows  that  we  may 
enumerate  as  (cost)  elements  of  price  the  following  as  important 
for  us : 

1.  The  cost  of  grounds. 

2.  The  cost  of  buildings,  machines,  and  other  fixed  capital 
costs  (Stehende  Sachkapitalkosten) . 

clearly.  It  is  necessary  to  keep  this  difference  in  mind  for  this  discussion  in  which 
wages  of  management  and  payment  of  risk  are  part  of  the  cost  of  production 
and  not  part  of  the  profits.  Weber  is  here,  as  throughout,  concerned  with  the 
"pure"  or  "static"  system  of  economics.  Cf .  above,  p.  lo. — Editor. 


3.  The  cost  of  securing  materials,  power  and  fuel. 

4.  The  cost  of  labor. 

5.  The  cost  of  transportation. 

6.  The  interest  rates. 

7.  The  rate  of  depreciation  of  fixed  capital.^ 
Which  of  these  elements  vary  according  to  the  location  of 

the  place  of  production  and  thus  represent  general  regional  fac- 
tors of  location?  Let  us  begin  with  the  last  one. 

1.  The  rate  of  depreciation  (and  therefore  of  amortization) 
of  the  fixed  capital  (7)  is  obviously  on  the  whole  independent  of 
geographical  situation.  Only  the  climatic  conditions  may  be  of  i 
importance,  for  example,  by  causing  a  greater  amount  of  rusti 

30  upon  the  machines  due  to  greater  humidity  of  the  air.  But  theses 
would  be  special,  not  general  regional  factors,  and  do  not  con- 
cern us  here. 

2 .  The  interest  rate  (6)  does  not  have  locational  significance« 
in  connection  with  the  process  of  production  in  the  territory  of  an,; 
economically  uniform  state  which  we  use  as  the  theoretical  basis- 
of  our  ''pure"  theory.  The  interest  rate  varies,  of  course,  accord- 
ing to  the  quality  of  the  enterprise  as  well  as  the  management;; 
thus  the  interest  rate  may  certainly  be  higher  as  the  consequence 
of  a  location  which  has  been  poorly  chosen  and  yields  a  question- 
able return.  But  it  does  not  vary  according  to  regions  within  as 
given  country  as  it  doubtless  does  for  different  countries  on  ac- 
count of  different  security,  different  wealth,  etc.^  It  can  never  be 
the  cause  of  regional  choice  of  location  in  the  pure  economic  sys- 
tem. In  fact,  it  does  not  even  show  significant  general  differences 
between  city  and  country,  (i.e.,  between  scattered  and  agglomer- 
ated industries)  within  such  a  political  system  as  the  German 

*  It  was  only  for  the  sake  of  thoroughness  that  we  did  not  present  this  group- 
ing at  the  outset. 

®  This  aspect  must  be  kept  very  clearly  in  mind  in  deaUng  with  locational 
problems  in  the  United  States.  There  is  good  ground  for  the  assumption  that 
these  elements  differ  from  state  to  state. — Editor. 


Commonwealth.  It  therefore  does  not  even  require  consideration 
as  an  agglomerative  factor  which  might  operate  within  a  given 
regional  distribution  of  industry. 

3.  The  cost  of  land  (i)  varies  in  the  case  of  industrial 
locations  according  to  the  amount  of  local  agglomeration,  but 
not  regionally — at  least  not  sufficiently  to  constitute  a  regional 
factor  of  location.  In  the  case  of  land  used  for  agriculture  the 
price  of  land  may  exercise  a  regional  influence.  The  prices  of  all 
other  types  of  land  have  significance  only  in  connection  with  ag- 
glomerations, for  they  represent  nothing  but  results  of  agglomer- 
ation and  deglomeration.  The  price  of  agricultural  land  may  be 
in  one  part  of  the  country  about  $50,  in  another,  $150,  in  a  third 
even  $250  or  $300  per  acre,  depending  upon  the  density  of  pop- 
ulation. This  will  be  a  matter  of  great  importance  in  determining  31 
the  kind  of  agricultural  production;"  but  for  the  choice  of  in- 
dustrial location  it  does  not  greatly  matter,  as  it  influences  the 
price  in  much  too  small  a  degree.  For  example,  if  a  modern  spin- 
ning mill,  which  requires  a  great  deal  of  space,  needs  2  ^  acres 
for  an  annual  production  of  1,200  tons  of  yarn,  it  is  almost  neg- 
ligible whether  $100^^  or  $500  will  have  to  be  paid  for  this  area. 

The  additional  $40  interest  per  annum  cause  an  additional 
3.3  cents  for  each  ton  of  yarn,  the  total  value  of  which  is  from 
$240  to  $800.  This  is  such  a  small  fraction  that  it  is  not  im- 
portant as  a  locational  factor.  Even  industries  with  a  low-priced 
product  and  very  large  space  requirements  (such  as  iron  works) 
are  insensitive  to  these  regional  differences  in  the  cost  of  land. 
Suppose,  for  example,  a  Thomas  steel  works  which  may  be  esti- 
mated to  require  250  acres  for  an  annual  production  of  300,000- 
I  400,000  tons^^  has  to  pay  $250  instead  of  $50  per  acre,  and  thus 

^°  Cf.  the  classical  treatment  of  Thünen,  Der  Isolierte  Staat,  Vol.  I,  which 
.  deals  with  this  problem. — Editor. 

I  "  Since  this  is  an  example  only,  dollars  and  cents  and  acres  have  been  sub- 

stituted for  Mark,  Pfennig,  and  Aar  on  a  rough  average. — Editor. 

"  Cf .  Heymann,  Die  gemischten  Werke  im  deutschen  Grosseisengewerbe 
(München,  1904),  p.  25. 


has  on  its  books  an  item  of  $62,500  instead  of  $12,500  for 
land.  The  difference  in  interest  on  $1,250  per  acre^^  causes  a 
difference  in  cost  of  $0,005  per  ton  of  product.  Since  this  ton 
has  a  value  of  about  $25,  the  difference  amounts  to  two-hun- 
dredths  of  i  per  cent.  This  difference  is  much  too  small  to  exer- 
cise any  influence  upon  the  location. 

The  situation  becomes  quite  different  if  local  agglomeration 
enters  into  the  picture  and  suddenly  creates  those  towering  rises 
to  $5,000,  $10,000  and  even  $50,000  per  acre.^*  Such  rises,  of 
course,  put  the  price  of  land  among  the  relevant  elements  of  cost 
of  industrial  production.  For  the  Thomas  steel  works,  for  exam- 
ple, they  would  mean  an  increase  in  the  cost  of  production  on  ac- 
count of  rent  (Preissteigerung  durch  Grundzins  kost  en)  amount- 
ing respectively  to  $0.125,  $0.25,  and  $1.00  per  ton.  These  are 
amounts  which  certainly  may  be  important,  and  on  account  of 
which  the  rent  will  codetermine  the  location  for  products  of  this 
32  kind.  It  is  a  locational  factor  within  the  agglomerative  tend- 
encies. But  it  need  not  be  considered  for  the  regional  factors. 

4.  The  cost  of  building,  the  cost  of  machines,  and  other 
equipment  (2),  and  the  cost  of  materials  and  power  supplies 
(4),  represent  nothing  but  the  results  of  the  price-making  of: 
(a)  the  production  of  raw  materials  and  power  supplies;  (6)  the 
previous  and  auxiliary  stages  of  industrial  production. 

Regarding  b,  they  are  for  purposes  of  our  reasoning  funda- 
mentally the  same  thing  as  the  particular  stage  of  production 
which  we  have  chosen  for  our  abstract  analysis.  Their  costs  may 
be  broken  up  into  the  same  elements  into  which  we  have  re- 
solved the  costs  of  that  stage.  The  previous  stages  contain  no 

^•'Why  Weber  should  use  an  interest  rate  of  2.5  per  cent  in  this  instance 
when  he  used  10  per  cent  in  the  previous  one  is  not  clear  from  the  text.  But  the 
reasoning  seems  to  hold  good,  even  if  the  difference  amounted  to  as  much  as 
0.08  per  cent,  as  it  would  if  an  interest  rate  of  10  per  cent  were  used. — Editor. 

"  Cf .,  for  example,  Andreas  Voigt,  Bodenbesitzverhaeltnisse,  etc.,  in  Berlin, 
regarding  the  rise  in  real  estate  values  in  Charlottenburg. 


new  elements  of  cost,  and  thus  no  new  and  unknown  locational 

Regarding  a,  there  remain,  then,  as  new  elements  of  cost  for 
our  consideration  the  prices  of  raw  materials  and  of  power,  and 
they  in  fact  represent  not  only  a  new,  but  apparently  a  geograph- 
ically varying,  element  of  cost,  that  is  to  say,  a  regional  factor 
of  location.  The  price  at  which  the  same  material  or  power  can 
be  acquired  may  be  and  will  be  different  at  its  various  places  of 
production,  depending  upon  the  nature  of  the  deposit,  the  dif- 
ficulties of  its  mining,  etc.  Depending  upon  which  particular 
"deposit,"  as  we  shall  call  it,  one  draws  for  his  particular  manu- 
facture, the  costs  of  raw  materials  and  power  materials  will 
vary.  It  will  obviously  depend  upon  the  location  of  the  plant 
whether  it  profits  from  the  lower  prices  of  a  certain  deposit  of 
materials.  Thus  geographically  determined  differences  of  cost 
influence  the  location.  These  differences  undoubtedly  represent 
.  the  first  general  regional  factor  of  location.  33 

I  5.  The  second  regional  factor  of  location  are  the  regionally 
differing  labor  costs  ( 5 ) .  It  goes  without  saying  that  their  locally 
different  level  pulls  production  to  and  from  certain  regions.  This 
is  achieved  by  the  costs  of  the  manufacturing  process  (Stoffum- 
wandlung) within  the  stage  of  production  here  under  considera- 
tion as  well  as  indirectly  by  the  prices  of  the  auxiliary  products 
which  are  partly  determined  by  such  labor  costs.  It  should  be 
,  remarked,  however,  that  we  mean  real  labor  costs. ^^ 
I  6.  We  come  finally  to  the  costs  of  transportation  (6)  which 
have  to  be  met  in  order  to  assemble  the  materials  and  to  ship  the 
finished  products.  It  is  obvious  that  transportation  costs  will 
vary  according  to  the  location  of  the  plant.  They  will  vary  ac- 
cording to  the  length  and  nature  of  the  road  which  the  materials 

^"The  German  text  reads  ".  .  .  .  dass  natürlich  nicht  die  absolute  Höhe 
der  Löhne  dabei  in  Frage  steht,  sondern  ihre  Höhe  bezogen  auf  irgend  eine 
Einheit  Produkt,  das  was  man  eben  heute  meint,  wenn  man  präzis  von  "Arbeits- 
kosten" spricht. — Editor. 


have  to  travel  from  the  place  of  production,  and  which  the  fin- 
ished products  have  to  travel  to  their  place  of  consumption. 
Sometimes  the  kind  of  transportation  system  will  make  a  differ- 
ence. These  costs,  then,  also  are  regional  factors  of  location  of  a 
general  kind. 


The  relative  price  range  of  deposits  of  materials,  the  costs 
of  labor  and  transportation,  then,  are  the  regional  factors  of  lo- 
cation of  every  industry.  Of  these,  we  may  for  purposes  of 
theoretical  reasoning  express  one,  the  relative  price  range  of 
deposits  of  materials,  by  another,  by  differences  of  costs  of  trans- 
portation. We  shall  thus  simplify  considerably  the  formulation 
of  our  theory,  since  we  shall  have  to  operate  with  only  two  re- 
gional factors. 

The  different  price  levels  of  different  deposits  of  the  same 
material  operate  as  if  one  had  to  oveicome  different  distances 
from  these  deposits  to  the  place  of  manufacturing,  or  as  if  the 
''cheap"  deposit  were  situated  nearer  the  plant,  and  the  "dear" 
deposit  farther  away.  In  order  to  see  this  clearly,  one  might 
imagine  an  average  price  as  the  normal  price  of  each  material  at 
34  the  deposit.  The  differences  in  the  price  at  this  or  that  deposit 
will  mean  the  same  thing,  from  the  point  of  view  of  the  indi- 
vidual plant,  as  if  additional  costs  of  transportation  had  to  be 
paid.  This  means  that  the  differences  of  the  price  of  material 
deposits  may  be  expressed  abstractly  as  differences  of  cost  of 
transportation.  We  need  not  treat  them  as  a  separate  locational 
factor,  but  may  introduce  them  later  as  a  modification  of  the 
effect  of  the  cost  of  transportation,  a  modification  which,  of 
course,  will  have  to  be  elaborated  considerably.^^  Consequently 
we  may  work  with  two  general  regional  factors,  the  costs  of 
transportation  and  of  labor. 

This  result  is  most  important  for  us.  Since  we  learned  before 

"  Cf.  below,  "approximations  to  reality,"  p.  74. 


that  all  general  locational  factors  which  are  not  of  a  regional 
kind  (i.e.,  all  the  rest)  can  only  be  agglomerative  or  deglomera- 
tive  factors,  we  may  treat  these  latter  factors  as  a  uniform  ag- 
glomerating force,  that  is,  as  a  third  uniform  locational  factor. 
We  may  thus  at  once  construct  our  entire  abstract  system  of 
general  locational  factors  and  the  theory  of  its  dynamics. 

Let  us  start  by  supposing  that  all  the  isolated  processes  of 
industrial  production  will  ''naturally"  at  first  be  pulled  to  their 
most  advantageous  (optimal)  points  of  transportation  costs.  Let 
us  then  regard  this  as  the  basic  network  of  industrial  orientation 
created  by  the  first  locational  factor,  transportation  costs.  Ap- 
parently, then,  the  differences  of  costs  of  labor  (the  second  loca- 
tional factor)  represent  a  force  altering  this  basic  network.  The 
most  advantageous  places  of  labor  costs  create  a  first  ''distor- 
tion" of  the  basic  transportational  (transportmässig)  network  of 
industrial  location.  We  thus  gain  the  conception  of  a  fundamen- 
tal orientation  of  industry  according  to  costs  of  transportation, 
and  of  an  alteration  of  this  fundamental  orientation  by  "labor 
locations"  (Arbeitsplätze).  35 

I  Every  agglomerating  tendency — in  other  words,  the  entire 
'group  of  all  other  locational  factors  which  we  have  not  so  far 
taken  into  account — is  nothing  but  a  second  altering  force,  an- 
I other  "deviating  tendency"  which  tends  to  distort  the  transporta- 
tional network  and  shift  it  to  certain  other  points,  the  "points 
of  agglomeration."  In  its  net  effect  this  entire  group  is  a  "unit" 
also.  And  like  the  other  "altering  factor,"  the  differences  in 
labor  costs,  it  is  a  uniform  "locational  factor."  It  is  competing 
with  that  other  factor. 

This  completes  the  theory  of  general  locational  factors  and 
the  general  survey  of  the  dynamics  within  which  they  work,  at 
least  to  the  extent  to  which  this  theory  and  survey  are  necessary 
as  a  basis  for  the  "pure"  theory  of  location.  There  are  no  other 
general  factors  influencing  the  location  of  industry.  The  only 


question  is  to  what  extent  and  according  to  what  laws  these  three 
factors  control  the  various  parts  of  the  industrial  system.  To 
show  this  will  be  the  task  of  the  pure  theory.  By  introducing  the 
agglomerating  factor  into  the  explanation  we  seek  to  make  an 
analysis  of  the  general  laws  controlling  the  locational  distribu- 
tion of  industry,  and  not  merely  those  connected  with  isolated 
36  processes  of  production. 




The  theory  to  be  given  here  is  to  explain  reality.  In  the  last 
chapter  we  have  seen  how  complicated  the  reahty  of  industrial 
location  is  rendered  by  the  interrelated  working  (Durcheinan- 
derwirken)  of  ''general"  and  ''special"  locational  forces.  But 
this  reality  is  further  complicated  by  the  fact  that  it  results  from 
the  interaction  {Hin-  und  Rückwirkung)  of  different  economic 
spheres  and  of  different  parts  of  the  same  sphere.  In  our  theory 
we  shall  ignore  certain  aspects  of  this  situation.  We  shall  assume 
that  some  of  the  facts  which  are  in  truth  brought  into  existence 
by  the  processes  which  we  analyze  are  independent  of  these 
processes.  After  having  reached  an  understanding  of  the  facts 
thus  isolated,  we  shall  introduce  the  full  causal  mechanism,  i.e., 
we  shall  bring  into  proper  perspective  isolated  data  and  shall 
analyze  the  change  which  is  created  thereby. 

On  the  basis  of  this  method,  industrial  orientation  will  be 
further  analyzed  within  the  limits  of  the  following  suppositions : 

I.  We  shall  assume  the  geographical  basis  of  materials  as 
something  given.  This  assumption  is  in  accordance  with  the 
facts  when  we  are  concerned  with  materials  like  stones,  minerals, 
etc.,  which  are  simply  dug  out  or  mined — which,  in  other  words, 
exist  at  different  places  by  nature.  The  assumption  is  not  quite 
so  correct  when  the  materials  employed  have  to  be  produced,  as 
is  true  of  agricultural  products.  The  agricultural  basis  of  indus-  37 
trial  materials  is  nothing  "given."  Agriculture  receives  its  geo- 
graphical location  by  a  peculiar  process  which  itself  depends 
upon  the  distribution  of  its  products,  that  is  to  say,  upon  the 



orientation  of  industry.   This  has  been  elaborately  shown  by 

In  placing  industry  for  the  time  being  theoretically  into  a 
given  geographical  ground  plan  of  material  deposits,  we  shall 
intentionally  neglect  the  retroactive  effect  {Rückwirkung)  which 
industry  may  exercise  upon  this  ground  plan.  This  assump- 
tion will  have  to  be  examined  and  brought  into  accord  with 
reality  later. 

2.  The  geographical  nature  of  the  sphere  of  consumption 
also  will  for  the  time  being  be  treated  as  a  given  phenomenon. 
The  situation  and  size  of  the  places  of  consumption  will  be  as- 
sumed in  the  pure  theory  as  a  given  framework  of  orientation. 
We  shall  thus  ignore  the  fact  that  each  locational  distribution 
of  industry,  merely  by  distributing  the  labor  forces,  distributes 
consumption  of  industrial  products  and  of  all  other  products. 
The  geographical  distribution  of  one  sphere  of  consumption, 
which  contains  industry  and  its  productive  connections,  is  itself 
partly  created  and  molded  by  this  industry. 

3.  Finally,  we  shall  not  introduce  the  mobility  of  the  labor 
basis  of  industry.  We  shall  operate  with  the  schematic  concept 
of  an  area  covered  by  several  fixed  labor  locations  (Arbeits- 
plätze) instead  of  introducing  the  shifting  distribution  of  hu- 
man labor  characteristic  of  present-day  reality.^  We  shall  fur- 
ther assume  that  the  wages  of  each  branch  of  industry  are 
''fixed,"  while  the  amount  of  labor  available  at  this  price  is  un- 
limited.^ Here  also  we  neglect  in  so  doing  a  part  of  reality,  for 
of  course  the  locational  tendencies  of  industry  themselves  create 
the  standard  of  wages  by  codetermining  the  local  demand  for 

^Johann  Heinrich  von  Thünen.  Der  isolierte  Staat  in  Beziehung  auf  Land- 
wirtschaft und  Nationalökonomie  (Rostock,  1842).   Cf.  p.  xix. — Editor. 

^  This  is  the  point  of  attack  of  Sombart.  Cf.  Der  Moderne  Kapitalismus, 
Vol.  II,  2  and  above,  p.  xxv. 

^The  details  regarding  these  suppositions  and  the  reasons  for  them,  may 
be  found  in  chap,  iii,  sec.  I,  toward  the  end. 


labor.  Moreover,  we  disregard  for  the  time  being  to  what  extent  38 
the  local  distribution  of  labor,  i.e.,  the  situation  and  size  of  labor 
locations,  is  generally  influenced  by  the  other  locational  tenden- 
cies of  industry.  We  evade  all  these  problems  for  the  moment  by 
assuming  a  given  basic  distribution  of  labor.  It  should  be  said  at 
once  that  it  will  become  apparent  that  this  third  assumption  can- 
not be  eliminated  within  the  scope  of  the  ''pure"  theory;  the  dy- 
namic relationship  between  the  local  distribution  of  labor  and  the 
locational  tendencies  of  industries  can  be  explained  only  by  the 
realistic  theory. 

Other  assumptions  and  simplifications  will  appear  necessary 
from  time  to  time,  but  all  of  them  will  accompany  us  for  but 
short  distances.  Only  the  three  simplifying  assumptions  just 
mentioned  are  permanent  and  constitute  the  matrix  within  which 
the  pure  theory  will  be  found. 


As  the  foregoing  analytic  examination  of  the  locational  fac- 
tors shows,  we  assume  in  our  theory  that  all  industrial  produc- 
tion is  dependent  upon  the  use  of  ''materials,"  which  are  either 
raw  materials,  half-finished  products,  or  power  supplies  (wood, 
coal).  We  speak  exclusively  of  the  use  of  "transportable"  ma- 
terials. In  fact,  however,  not  only  materials  enter  into  produc- 
tion, but  "forces  of  nature"  as  well.  They  are  used  as  live  energy: 
either  given  by  nature,  like  water  power,  or  transformed,  like 
electricity.  The  question  is  whether  a  theory  which  employs  the 
concept  of  transportable  materials  only  can  include  the  loca- 
tional effect  of  those  other  forces  as  well.  The  answer  is  that 
apparently  it  is  possible  to  treat  these  forces  of  nature  with  re- 
gard to  their  locational  influence,  as  if  they  were  especially  cheap 
coal  deposits.  If  that  is  done — how  it  has  to  be  done  is  shown  in 
the  last  sections  of  the  chapter  on  transport  orientation — we  39 
shall  get  rules  determining  the  locational  importance  of  these 


forces.  These  rules  modify  only  slightly  the  general  rules  which 
apply  when  transportable  materials  are  employed. 

Thus  no  specific  effect  which  could  not  be  fitted  into  the  the- 
ory remains.  This  theory,  then,  embraces  in  its  simple  mold  in- 
dustry in  its  entirety,  with  all  the  materials  and  forces  which  it 
40  absorbs  into  itself. 






The  problem  to  be  solved  is  how  transportation  costs  in- 
fluence the  distribution  of  industries,  assuming  that  no  other 
factors  influencing  the  location  of  industry  exist.  To  what  places 
will  industry  be  attracted?  It  is  clear  that  it  will  be  drawn  to 
those  locations  which  have  the  lowest  costs  of  transportation, 
having  regard  both  for  the  place  of  consumption  and  the  place  of 
the  deposits  of  materials.  Where  are  these  places?  At  first  we 
shall  locate  them  in  very  general  terms,  and  to  that  end  we  in- 
quire: On  what  basic  elements  do  transportation  costs  depend? 

The  fundamental  factors  which  determine  transportation 
costs  are  the  weight  to  be  transported  and  the  distance  to  be 
covered.  Since  these  two  factors  may  readily  be  defined  in  math- 
ematically exact  terms,  they  provide  a  definite  basis  for  an  ab- 
stract theory,  leading  possibly  to  mathematical  formulas.  We 
shall,  at  the  outset,  treat  these  two  factors  as  the  only  determin- 
ing factors.  This  procedure  is  justified  because  we  are  thinking 
of  costs  in  an  economic  sense.  There  are,  of  course,  two  kinds  of  41 
"transportation  costs:"  transportation  costs  in  the  sense  of  pohti- 
cal  economy,  and  transportation  costs  as  understood  by  the  busi- 
ness man  paying  for  the  shipment  of  goods.  The  former  costs 
are  the  total  amount  of  goods  and  labor  that  are  absorbed  in 
effecting  such  a  shipment.  The  latter  costs  are  the  monetary  pay- 
ment made  to  those  furnishing  the  transportation.^  If  we  speak 

^  This,  in  English  terminology,  would  commonly  be  termed  the  rate  or  the 
price  of  transportation.  Cf .  also  Emil  Sax,  Die  Verkehrsmittel,  2d  ed,  I,  76  ff.  The 



of  weight  and  distance  as  the  fundamental  factors  determining 
transportation  costs  we  obviously  have  in  mind  the  costs  of 
''pure"  political  economy. 

Our  further  discussion  is  based  upon  the  possibility  of  ex- 
pressing in  terms  of  weight  and  distance  all  other  factors  which 
contribute  to  the  cost  of  transportation,  limiting  our  considera- 
tion to  an  area  with  a  uniform  system  of  transportation.  Because 
of  this  possibility  we  are  able  to  reduce  the  other  factors  theoret- 
ically to  these  two. 

What  this  means  and  why  it  is  the  case  requires  a  brief  ex- 
planation. In  this  connection  it  should  be  noted  that  the  trans- 
portation system  analyzed  here  is  the  railway  system  prevailing 
today  and  the  particular  rate  structure  existing  in  Germany.  The 
railroad  system  has  been  chosen  for  our  analysis  of  the  causal 
relationship  between  the  cost  of  transportation  and  the  distribu- 
tion of  industries  over  a  territory  because  the  railroad  is  today 
the  chief  means  of  transportation  by  land.  As  a  device  for  simpli- 
fying our  problem,  we  shall  proceed  as  if  it  were  the  only  system 
42  existing.^  The  significance  of  the  relationship  between  carriers 
subject  to  different  principles  of  cost  determination  will  be  ex- 
amined later  when  our  abstractions  are  brought  into  accord  with 

It  is  clear  that  the  cost  of  transportation  depends  upon  the 
following  factors,  besides  weight  and  distance:  ( i )  The  type  of 
the  transportation  system  and  the  extent  of  its  use;  (2)  the  na- 
ture of  the  region  and  its  kind  of  roads;  (3)  the  nature  of  the 
goods  themselves,  i.e.,  the  qualities  which,  besides  weight,  deter- 
mine the  facility  of  transportation. 

problem  of  joint  cost  is  discussed  by  F.  W.  Taussig,  "A  Contribution  to  the 
Theory  of  Railway  Rates,"  Quarterly  Journal  of  Economics,  V,  438,  and  A.  C. 
Pigou,  The  Economics  of  Welfare,  p.  266-68. — Editor. 

^The  same  analysis  could  be  undertaken  for  any  other  rate  structure  and 
any  other  system  of  transportation,  but  it  is  not  necessary,  because  the  prin- 
ciple is  the  same  everywhere. 


Taking  up  the  first  point,  it  hardly  needs  to  be  explained  that 
the  type  of  the  transportation  system  and  the  extent  of  its  use 
produce  great  differences  in  cost  as  among  the  different  systems. 
A  given  weight  is  carried  a  given  distance  today  on  railroads  for 
one-quarter  to  one-tenth  of  the  rate  prevailing  when  carriages 
had  to  be  used.  The  costs  must  have  dropped  correspondingly. 
However,  different  systems  of  transportation  do  not  concern  us 
for  the  present,  since  we  are  assuming  a  uniform  system. 

But  even  in  a  uniform  system  the  different  parts  of  the  sys- 
tem are  used  with  varying  intensity,  and  this  varying  intensity 
causes  differences  in  the  cost  of  transporting  a  given  weight  a 
given  distance.  The  shipping  of  one  hundred  tons  of  coal  costs 
more  on  a  road  when  a  special  freight  train  must  be  made  up  for 
the  purpose  than  when  an  existing  train  can  carry  an  additional 
hundred  tons.  Similarly  the  costs  will  be  higher  when  there  is 
no  return  freight  than  when  return  freight  is  always  available. 
So  also  the  costs  per  ton-mile  vary,  even  on  the  same  road,  ac- 
cording to  the  volume  of  traffic.  These  are  well-known  facts.  It 
is  also  known,  however,  that  it  is  so  difficult^  to  calculate  individ- 
ually the  resulting  differences  in  the  cost  of  shipping  individual 
articles,  that  these  differences  are  disregarded  in  the  rate-making 
of  our  present  uniform  railroad  system,  and  the  rates  are  fixed  43 
uniformly  per  ton-mile  for  all  Hues.  Since,  in  making  its  rates, 
our  system  of  transportation  disregards  these  variations  from 
a  cost  caluculated  according  to  weight  and  distance,  they  may  be 
disregarded  in  our  theory.  But  if  in  fact  such  variations  of  rates 
should  exist,  the  problem  arising  should  be  solved  by  assuming 
that  lines  with  higher  rates  are  prolonged  in  proportion  to  the 
higher  rate;  and  similarly,  lines  with  lower  rates  should  be  as- 
sumed to  be  shortened.  If,  for  example,  on  certain  lines  a  one- 
and-a-half  rate  per  ton-mile  is  collected  instead  of  the  normal 
rate  of  one,  such  lines  should  be  regarded  as  one-and-a-half  times 
as  long  as  they  really  are  in  applying  to  them  a  theory  of  location 

^  For  this  point,  cf .  Taussig. — Editor. 


which  assumes  uniform  rates.  In  Germany  conditions  do  not, 
on  the  whole,  call  for  this  method  of  treatment. 

There  is,  however,  another  aspect  to  this  matter,  an  aspect 
in  which  the  interest  of  the  carriers  in  the  greatest  possible  utili- 
zation of  their  facilities  is  reflected  in  the  rates.  Higher  rates  per 
mile  prevail  generally  for  small  shipments  and  for  shipments 
over  short  distances.  This  is  not  the  place  to  show  how  and  when 
these  adjustments  result  from  the  necessity  of  increasing  the 
density  of  traffic,  nor  to  show  how  they  relate  to  the  lowering  of 
general  operating  expenses  per  unit  carried.  Since  such  adjust- 
ments do  exist,  the  problem  they  place  before  us  is  this:  How 
may  they  be  disposed  of  in  treating  cost  of  transportation  merely 
as  a  function  of  weight  and  distance? 

No  serious  problem  is  raised  by  rates  which  decrease  as  the 
distance  increases.  The  same  theoretical  principle  as  before  can 
be  used  here;  the  distance  can  be  thought  of  as  varying  accord- 
44  ing  to  the  percentage  of  the  decrease  whenever  such  scales  apply. 
Geographical  distances  should  not  be  measured  by  their  geo- 
graphical length,  but  in  proportion  to  the  decreasing  rate  scale.* 

The  problem  raised  by  the  difference  in  rates  between  par- 
cels, half-carloads,  and  full  carloads,  is  best  solved  by  regarding 
those  charges  which  are  made  on  full  carloads  as  the  normal  ton- 
mile  rates.  Then  those  goods  which  are  charged  higher  rates 
because  they  are  shipped  in  small  quantities  can  be  regarded  as 
possessing  an  ideal  weight  in  addition  to  the  real  weight.  For  in- 
stance, if  the  normal  rate  for  full  carloads  is  6  cents,  the  rate  for 
half-carloads  6.7  cents,  and  the  rate  for  parcels,  11  cents,  goods 
not  shipped  in  full  carloads  may  be  regarded  as  having  an  addi- 

*  If,  as  in  the  case  of  parcel  rates  in  the  general  class  in  Germany,  a  rate  of 
II  pfennig  is  charged  per  unit  of  weight  for  50  kilometers,  10  for  the  next  150, 
and  9  for  the  next  100,  and  so  on,  a  stretch  of  100  is  counted  as=5o4-  (So- 
50/11)  =  95.4  km.  We  may  say,  then,  that  the  geographical  distance  is  corrected 
in  proportion  to  the  rates;  an  operation  which,  by  the  way,  the  present  German 
rate  structure  fortunately  spares  us  to  a  large  degree.  It  provides  a  graded  scale 
of  rates  only  for  some  of  the  parcels  and  for  a  few  bulk  goods. 


tional  "ideal"  weight  amounting  to  i.i  per  cent  and  83.3  per  cent 
respectively  of  their  real  weight.  Similarly,  the  weight  of  goods 
shipped  on  special  reduced  rates  may  be  thought  of  as  being  re- 
duced in  proportion  to  the  reduction  in  rates. 

In  this  way  it  seems  possible  for  theoretical  purposes  to  ex- 
press in  terms  of  weight  and  distance  all  variations  in  rates,  and  45 
thus  to  fit  them  without  difficulty  into  a  theory  based  on  weight 
and  distance  alone.  The  general  principle  of  this  approach  to  the 
matter  is  clearly  based  on  the  fact  that  the  effect  of  all  elements 
of  cost  will  appear  as  increase  or  reduction  of  the  rate  per  ton- 
mile.  This  justifies  operating  theoretically  with  weight  and  dis- 
tance, the  two  basic  elements  of  the  cost  of  transportation. 

In  passing  we  may  apply  this  method  to  the  other  two  most 
important  instances  of  variations  of  cost  as  mentioned  before. 

The  second  factor  upon  which  cost  of  transportation  de- 
pends, aside  from  weight  and  distance,  is  the  nature  of  the  local- 
ity, influencing  the  road  bed  (see  p.  42).  On  the  one  hand  the 
nature  of  the  locality  determines  the  cost  of  road  construction, 
and  on  the  other  hand  it  affects  the  cost  of  operation.  Obviously, 
these  local  increases  or  decreases  of  cost,  reflected  in  ton-mile 
rates,  may  be  expressed  by  prolonging  or  shortening  the  sections 
in  question  proportionally.  They  therefore  offer  no  particular 
difficulty  for  our  theory.  Moreover,  the  management  of  modern 
railway  systems  operated  under  consolidated  control  usually 
ignores  these  differences  in  cost.  For  instance,  rates  in  Germany 
are  uniform,  regardless  of  the  special  cost  both  of  construction 
and  of  operation  of  different  sections  of  the  system.  In  our  later  46 
inductive  examination  of  location  we  are  not  dealing  with  moun- 
tains and  valleys,  but  with  a  mathematically  flat  plain  where  the 
mountains  are  razed,  the  valleys  filled,  and  the  swamps  covered. 
The  rate  structure  of  the  German  railroads  realizes  the  "ideal"; 
we  shall  utilize  it  in  our  work  and  thus  simplify  our  deductions. 

The  third  factor  affecting  cost  of  transportation,  aside  from 
weight  and  distance,  is  that  of  special  qualities  of  the  goods  trans- 


ported.  Bulky  goods  require  more  space,  and  thus  increase  the 
cost  by  requiring  more  rolling  stock.  Perishable  and  explosive 
goods  necessitate  great  care,  not  only  in  loading,  but  also  in  car- 
rying them.  All  such  qualities  result  in  higher  rates  per  ton. 
Moreover,  certain  kinds  of  goods  are  given  higher  rates,  which, 
because  of  the  high  value  of  the  goods,  do  not  increase  costs  par- 
ticularly. Indeed,  there  exist  systems  of  rate-making  which, 
disregarding  weight,  take  for  their  basis  value  and  distance.  In 
fact,  however,  all  so-called  value  rate-schedules  {Werttarife)  are 
really  based  on  weight,  even  though  disguised  by  scales  of  value. 
But  it  does  not  concern  us  here  whether  scales  based  on  value  are 
justified,  since  the  transportation  of  an  object  requires  the  same 
cost  whatever  the  value.^  Suffice  it  for  us  to  know  that  such 
scales  exist.  They  do  not  cause  us  any  difficulty.  An  increase  in 
47  the  rate  per  ton-mile,  no  matter  for  what  reason,  means  added 
''ideal"  weight,  a  decrease  means  subtracted  "ideal"  weight;  that 
is  all.^ 

All  the  foregoing  is  perfectly  simple.  We  have  not  only  dem- 
onstrated clearly  the  principle  in  accordance  with  which  the  im- 
portant factors  determining  cost  may  be  expressed  in  the  two 
basic  factors  of  weight  and  distance,  but  also  the  practical  exe- 
cution of  this  principle  for  all  cases  important  in  the  making  of 
railway  rates  today.  The  only  question  that  might  be  raised  is 

^  Cf.  for  this  discussion,  Sax,  Verkehrsmittel,  p.  76  ff.  and  100  ff.,  and  par- 
ticularly F.  W.  Taussig,  op.  cit.;  also  J.  W.  Clark,  The  Economics  of  Overhead 
Costs. — Editor. 

*  The  German  railway  freight  tariff  assigns  to  "bulky  goods"  one  and  one- 
half  times  their  actual  weight,  and  we  may  consider  them  as  having  this  weight. 
In  the  German  system,  value  is  taken  into  consideration  when  certain  commodi- 
ties of  low  value  are  shipped  at  lower  rates  than  is  usual.  Thus  certain  parcels 
of  low  value  are  shipped  at  8  pfennig  instead  of  11,  and  carloads  of  certain  goods 
of  small  value  at  4.5,  3.5,  and  2.6  instead  of  6  pfennig.  Here  again,  subtractions 
in  weight  may  be  made  in  our  calculations  corresponding  to  these  reductions ;  for 
instance,  coal,  which  is  shipped  at  2.6  pfennig  instead  of  6  pfennig  may  be  rated 
as  if  it  had  lost  56  per  cent  of  its  real  weight  when  we  come  to  applying  our 
theoretical  findings  to  German  reality. 


whether  the  deviations  from  the  uniform  rate  based  on  weight 
and  distance  and  the  adjustments  resulting  therefrom  are  not  so 
large  (particularly  in  other  transportation  systems)  that  it  is 
impractical  to  express  theoretically  all  transportation  costs  in 
weight  and  distance.  In  answer  to  this  we  may  say  two  things : 

First,  weight  and  distance  are  not  only  the  basis  of  railroad 
rates  but  are  the  predominant  factors  in  the  cost  of  transporta- 
tion, and  hence  of  rate-making  in  any  system,  since  they  largely 
determine  how  much  labor  is  necessary.  This  labor,  regardless  of 
its  nature,  is  the  essential  factor  of  cost,  and  consequently  of  rate- 
making.  An  abstraction  based  on  it  is  accordingly  in  no  real  48 
danger  of  giving  a  distorted  picture  of  reality  through  being  dis- 
torted by  the  influence  of  other  factors. 

Second,  the  rate  structure  as  it  exists  in  Germany  today  ap- 
proximates closely  the  abstraction  just  made.  The  German  rail- 
roads use  the  ton-mile  rate  as  the  general  basis,  calculating  rates 
according  to  weight  and  distance.  The  whole  country,  as  has 
been  said  before,  is  regarded  as  a  mathematically  flat  surface. 
They  employ  merely  "ideal"  weight  additions   (Gewichtszu- 
schläge) for  half -carloads  and  parcels,  as  well  as  for  bulky  and 
explosive  goods;  and  on  the  other  hand  they  employ  ''weight  re- 
ductions" (Gewichtsabzüge)  for  the  large  and  important  classes 
3f  goods  of  low  value.  They  employ  special  rates  modifying  the 
jniform  ton-mile  rates  only  for  certain  sections,  and,  as  men- 
ioned  before,  a  restricted  use  is  made  of  decreasing  scales  with 
ncreasing  distance  for  parcels  and  a  few  bulky  goods  of  low 

Reality,  then,  will  not  be  too  greatly  distorted  by  our  ab- 
straction. It  seems  quite  admissible  to  work  with  weight  and  dis- 
ance  in  theory  as  well  as  in  practice;  in  short,  to  work  with  the 
on-mile  rate  as  the  basic  scale  of  transportation  costs,  at  least 
n  a  territory  with  one  uniform  system  of  transportation.  The 
ustification  in  both  theory  and  practice  for  this  simplifying  as- 
umption  of  the  existence  of  a  uniform  system  of  transportation 


may  be  taken  for  granted  for  the  time  being,  for  we  shall  show 
later  on  that  the  more  complicated  situation  of  several  co-operat- 
ing transportation  systems  can  also  be  explained  in  accordance 
with  the  theory  here  developed. 



If  weight  and  distance  are  the  only  two  determining  factors, 
evidently  transportation  costs  will  draw  industrial  production  to 
those  places  where  the  fewest  ton-miles  originate  during  the  en- 
tire process  of  production  and  distribution;  for  with  production 
at  these  places  the  costs  of  transportation  will  be  lowest. 

But  how  will  the  places  of  minimum  ton-miles  actually  dis- 
tribute the  production?  That  is  the  real  question  to  be  answered. 

In  order  to  answer  it,  the  simplifying  assumptions  of  the 
whole  theory  set  forth  in  the  last  part  of  the  preceding  chapter 
must  be  kept  in  mind.  We  are  to  regard  as  given  the  location  and 
the  size  of  the  places  of  consumption  of  each  kind  of  produc- 
tion; and  we  are  to  regard  as  given  the  location  of  the  available 
material  deposits.  Furthermore,  for  the  time  being  (up  to  chap, 
vi)  we  proceed  upon  the  assumption  that  each  product  will  be 
produced  in  one  stage  of  production,  the  raw  material  being 
turned  into  the  finished  product  at  some  single  place  of  produc- 


Let  us  then  imagine  ourselves  stationed  at  some  one  of  these 
given  places  of  a  given  amount  of  consumption.  Clearly,  viewed 
from  this  place,  there  must  be  for  every  kind  of  product  con- 
sumed at  this  place  certain  deposits  of  materials  (raw  materials., 
power  materials)  the  use  of  which  will  result  in  the  lowest  trans- j 

50  portation  costs. 

By  no  means  will  these  deposits  necessarily  be  those  locatec 
nearest  to  the  place  of  consumption.   It  is  possible  that  in  the 


case  of  certain  materials  a  position  near  deposits  of  other  ma- 
terials is  more  important  (bearing  in  mind  the  cost  of  transpor- 
tation resulting  from  the  whole  process)  than  a  position  near  the 
place  of  consumption.  In  such  a  case  that  position  will  be  chosen 
which  is  optimal.  In  any  event,  viewed  from  each  place  of  con- 
sumption, there  doubtless  exists  for  each  kind  of  product  a  most 
advantageous  location  of  each  material  that  is  utilized  in  making 
the  product.  Obviously,  the  deposits  thus  most  advantageously 
located  will  be  employed  for  such  production  as  is  necessary  to 
fulfil  the  demand  at  the  particular  place  of  consumption.  The 


Fig.  2  Fig.  3 

location  of  the  place  of  production  must  be  determined  somehow 
in  some  relationship  to  the  place  of  consumption  and  to  these 
most  advantageously  located  material  deposits.  Thus  ''locational 
figures"  are  created,  one  for  each  place  of  consumption  of  each 
product.  This  locational  figure  is  formed  (as  indicated  above) 
by  the  place  of  consumption  and  the  most  advantageous  mate- 
rial deposits.  Each  product  will  somehow  select  its  place  of  pro- 
duction (location)  in  terms  of  this  figure. 

Let  us  suppose,  for  example,  that  we  are  dealing  with  a  prod- 
uct composed  of  two  materials  which  are  to  be  found  in  scattered 
deposits.  In  such  a  case  the  "locational  figures"  would  be  repre- 
sented by  triangles.  One  comer  of  each  triangle  would  be  the 
Dlace  of  consumption,  and  the  other  two  corners  would  be  the 
two  most  advantageous  places  of  material  deposits,  as  shown  in 
figures  i,  2,  and  3. 

Assuming  that  nothing  but  the  cost  of  transportation  influ- 
ences the  selection  of  the  location,  it  is  evident  that  these  loca- 


tional  figures  must  give  the  only  possible  mathematical  basis  of 
orientation.  This  presupposes,  however,  that  location  could  be 
divided,  as  a  matter  of  analysis,  into  just  as  many  parts  as  the 
locational  figures  contain.  We  can  presuppose  this  because  we 
are  disregarding  for  the  present  all  agglomerating  and  deglomer- 
51  ating  factors. 

These  'Vocational  figures"  therefore  represent  the  first  and 
most  important  basis  for  formulating  {vorstellen)  the  theory. 
We  shall  apply  these  figures  to  the  most  complicated  sets  of  facts 
because  through  their  use  the  outstanding  elements  of  the  struc- 
ture of  orientation  are  laid  bare. 

How  is  production  oriented  in  terms  of  these  locational  fig- 
ures? A  general  observation  must  be  made  before  proceeding  to 
answer  this  question.  The  main  features  of  the  orientation  of 
production  must  be  the  same  in  all  individual  locational  figures, 
no  matter  what  the  industry  may  be.  For  in  all  of  these  figures 
the  main  features  of  the  orientation  of  production  depend  upon, 
and  are  determined  by,  the  nature  of  the  transportation  needed 
for  the  particular  industry.  It  follows  that  in  order  to  find  the 
principles  according  to  which  one  may  locate  the  theoretical 
point  where  transportation  costs  are  lowest,  it  is  sufiicient  in  a 
theoretical  analysis  to  deal  with  a  single  locational  figure. 

Then,  too,  before  we  can  go  on  we  must  introduce  some  new 
terms.  They  refer  to  the  nature  of  the  materials  employed  by 
industry:  (a)  the  nature  of  their  deposits,  and  {b)  the  nature 
of  their  transformation  into  products.  It  will  become  apparent 
that  the  ''transportational  nature"  of  various  industries  depends 
entirely  upon  these  facts. 

As  regards  the  nature  of  the  material  deposits,  some  ma- 
terials employed  in  industry  appear  everywhere;  they  are,  for 
practical  purposes,  put  at  our  disposal  by  nature  without  regard 
to  location.  When  the  whole  earth  is  considered  this  actually 
holds  true  only  in  the  case  of  air;  but  when  more  limited  regions 
are  considered,  it  holds  true  for  many  other  things.  Brick-clay. 


wood,  grain,  etc.,  are  materials  available  practically  everywhere  . 
in  certain  regions.  Such  materials  will  be  called  ''ubiquities";  in 

I  the  former  case  ''general,"  in  the  latter,  "regional."  Naturally 
they  will  be  available  or  producible  in  each  place  only  in  limited 
quantities ;  nevertheless  it  is  possible  that  the  local  demand  does 
not  exceed  the  limits  of  their  supply,  and  in  that  case  they  are 
practically  "absolute  ubiquities."  If  the  demand  does  exceed 
this  limit,  they  are  "relative  ubiquities"  for  the  place,  the  region, 
etc.  Thus,  water  is  a  practically  unlimited,  and  therefore  an  52 
"absolute"  ubiquity  in  many  German  regions;  hkewise  brick- 
clay  for  certain  large  regions.  Grains,  on  the  other  hand,  are 
naturally  only  "relative  ubiquities"  for  all  territories  which  im- 
port grains.  "Ubiquity"  naturally  does  not  mean  that  a  commod- 
ity is  present  or  producible  at  every  mathematical  point  of  the 
country  or  region.  It  means  that  the  commodity  is  so  extensively 
available  within  the  region  that,  wherever  a  place  of  consump- 
tion is  located,  there  are  either  deposits  of  the  commodity  or  op- 

iportunities  for  producing  it  in  the  vicinity.  "Ubiquity"  is  there- 
fore not  a  mathematical,  but  a  practical  and  approximate,  term 
(praktischer  ''Näherungsbegriff'')  J 

Other  materials  are  not  obtainable  in  the  vicinity  of  a  place 
of  consumption  (irrespective  of  where  it  may  lie  within  the  coun- 
try or  the  region  which  is  made  the  object  of  locational  analysis) , 
but  only  in  geographically  well-defined  localities.  Or,  if  they  are 
technically  obtainable,  they  are  in  fact  mined  or  are  produced  by 
agriculture  only  in  well-defined  locaHties  because  of  economic 

:  reasons.  We  find  that  minerals  and  coal,  as  well  as  most  of  the 
.substances  which  are  used  for  chemical  and  china  manufacture, 

1  jbelong  in  the  former  category  of  technically  locahzed  materials, 
while  wood  and  wool  belong  in  the  category  of  the  economically 
ocaHzed  materials. 

It  is  obvious  that  it  is  not  predetermined  for  all  time  whether 

'Regarding  O.  Englander's  critical  discussion  of  this  concept  cf.  above,  p. 
Kiv,  n.  31. 


an  industrial  material  is  "localized"  or  "ubiquitous";  this  must 
be  determined  within  each  area,  country,  or  region,  for  the  period 
which  is  made  the  object  of  locational  analysis.  Let  us  take  for 
example  the  southeast  of  the  United  States.  For  that  region 
(perhaps! )  cotton  is  ubiquitous  from  a  practical  standpoint;  but 
evidently  it  is  not  ubiquitous  for  the  world  at  large.  For  Ger- 
many cotton  represents  the  reverse  of  a  ubiquity;  it  is  a  material 
which  must  be  brought  in  from  very  distant  places  outside.  It  is 
evident  also  that  all  relatively  ubiquitous  materials  belong  in  the 
sphere  of  localized  materials  if  at  a  given  place  the  demand  for 
them  or  for  any  of  their  parts  exceeds  the  amount  obtainable  at 
53  that  place.  Barley  is  a  case  in  point  in  so  far  as  the  demand  for 
it  in  breweries  exceeds  the  production  within  the  "vicinity"  of 
the  brewery. 

As  regards  the  nature  of  the  transformation  of  materials  into 
products,  a  material  enters  into  a  product  either  with  or  without 
residues.  These  residues  may  be  used  for  another  product,  but 
they  are  refuse  from  the  point  of  view  of  the  first  product.  In 
order  to  have  a  term  for  this  distinction  we  may  speak  of  "pure 
material"  and  "gross  material."  Any  ubiquitous  material  can 
naturally  be  either  pure  or  gross.  But  since  this  distinction  has 
no  significance  for  location  in  the  case  of  the  ubiquities,  the 
terms  "pure  material"  and  "gross  material"  will,  for  the  sake  of 
brevity,  be  used  only  for  "localized"  materials. 

Another  distinction  may  be  made  regarding  transformation 
of  material  into  a  product,  as  follows:  "pure  material"  imparts 
its  total  weight  to  the  product;  "gross  material,"  only  a  part  of 
it.  Consequently  we  may  consider  fuels  (such  as  wood,  coal, 
etc.)  when  used  for  production  as  the  extreme  case  of  gross  ma- 
terials, for  not  a  single  bit  of  their  weight  enters  into  the  product. 
They  create  important  chemical  and  mechanical  changes,  but 
their  use  adds  no  weight  to  the  product;  their  entire  weight,  from 
the  point  of  view  of  the  location,  remains  behind — "outside."  It 
is  desirable  for  our  purposes  that  such  materials  be  classified 


under  the  general  heading  of  "weight-losing"  materials,  together 
with  the  other  gross  materials  which  technically  play  a  funda- 
mentally different  role  in  production.  There  are  therefore  two 
kinds  of  gross  materials:  the  fuel  which  leaves  its  total  weight  as 
a  residue  outside  of  the  product,  and  the  gross  materials  which 
leave  only  a  part  of  their  weight.  It  is  apparent  that  it  is  very 
important  for  our  theory  to  have  covered  these  two  distinct  kinds 
of  materials  with  one  term,  for  the  simple  reason  that  we  are 
dealing  at  present  with  the  effects  of  weight  only.  54 

The  materials  used  by  industry  are,  for  the  purposes  of  the 
following  analysis,  either  "ubiquities"  or  "localized  materials"; 
and  these  latter  either  "pure  materials"  or  "weight-losing  ma- 


We  have  said  that  production  will  be  oriented,  under  the  in- 
fluence of  costs  of  transportation,  in  terms  of  the  "locational 
figures"  which  we  have  discussed.  In  view  of  our  explanation  of 
I  these  figures,  this  statement  means  that  production  must  find  the 
points  of  minimum  ton-miles.  These  points  will  be  the  trans- 
portational  locations. 

How  are  they  to  be  found?  The  fact  from  which  we  start  is 
that  such  a  location,  wherever  it  may  lie,  always  shows  the  fol- 
lowing transportational  relations:  the  entire  weight  of  the  ma- 
terials which  are  used  in  the  production  must  be  moved  to  this 
location  from  the  material  deposits;  and  the  weight  of  the  prod- 
uct must  be  moved  away  from  this  location  to  the  place  of  con- 
sumption. This  means  that  this  location  is  connected  with  the 
"corners"  of  the  locational  figures  by  lines  along  which  move  the 
weights  which  appertain  to  these  corners  (the  weights  of  the 
material  and  the  product  respectively).  Along  the  lines — let  us 
icall  them  "components" — of  the  material  deposits  run  the  re- 
spective material  weights,  and  along  the  component  of  the  place 


of  consumption  runs  the  weight  of  the  product.  Let  us  imagine 
a  process  of  production  which  uses  two  locahzed  materials,  three- 
fourths  of  a  ton  of  the  one  and  one-half  ton  of  the  other  being 
necessary  in  order  to  produce  one  ton  of  the  product.  The  loca- 
tional  figure  shows  the  weights  three-fourths  and  one-half  mov- 
ing along  the  components  of  the  two  materials;  while  the  com- 
ponent of  consumption  carries  the  weight  one.    (See  Fig.  4,  p. 


These  weights  represent  the  force  with  which  the  comers  of 
the  locational  figures  draw  the  location  toward  themselves,  it 
being  assumed  that  only  weight  and  distance  determine  transpor- 
ts tation.  For  any  movement  of  the  location  along  a  component 
toward  a  corner  saves  just  as  much  as  the  movement  amounts  to 
in  ton-miles.  And  if  orientation  takes  place  solely  in  accordance 
with  ton-miles,  the  importance  of  every  corner  will  be  propor- 
tional to  the  ton-miles  which  can  be  saved  by  approaching  it,  i.e., 
the  distance  between  the  location  and  a  given  corner  will  be  de- 
termined by  the  weight  which  attracts  along  its  locational  com- 
ponent. It  follows  as  a  general  principle  that  the  location  will  be 
near  the  individual  corners  or  jar  from  them  according  to  the 
relative  weight  of  their  locational  components. 

The  mathematician  (cf.  Mathematical  Appendix  I,  §2)  tells 
us  that  the  precise  location  within  the  figures  can  be  determined 
mechanically  by  means  of  a  frame  (Varignon's  frame;  cf.  picture 
in  Appendix  p.  229).  The  corners  of  this  frame  are  to  be  set  up 
at  the  corners  of  the  locational  figure.  Over  these  corners  run 
threads  on  rollers,  the  threads  being  loaded  with  weights  propor- 
tional to  the  weights  of  the  components.  In  the  inner  part  of  the 
figure  these  threads  are  connected  at  some  point.  Wherever  this 
connecting  point  (which  must  be  prevented  from  being  drawn 
beyond  one  of  the  corners)  comes  to  rest,  there  is  the  location. 
This  location  point  may  be  in  one  of  the  corners,  if  one  of  the 
weights  is  of  the  necessary  size,  or  if  a  peculiar  geographical  con- 
dition prevails ;  otherwise,  it  will  be  found  somewhere  within  the 




On  the  basis  of  the  same  general  concept  (Allgemeinvor- 
stellung) in  accordance  with  which  the  location  is  mechanically 
determined,  '^weight  figures"  can  be  mathematically  deduced  for 
any  kind  of  production.  While  the  locational  figures  will  always 
be  individual  or  specific  for  a  particular  plant,  these  weight  fig- 
ures are  general,  applying  to  all  plants  of  the  same  kind  of  pro- 
duction. Such  weight  figures  are  formed  by  line  segments  whose 

Fig.  5 

Fig.  6 

length  is  proportional  to  the  size  of  the  weights  which  attract 
along  the  components  of  the  locational  figure  of  a  particular 
productive  enterprise.  If  the  locational  figure  is  a  triangle,  and  56 
if,  as  in  the  previous  example  the  component  weights  are  i=ai, 

J4=a2,  y2=(i3,  then  we  can  construct  a  weight  figure  which 
looks  like  Figure  5. 

The  following  propositions  regarding  the  position  of  the  lo- 
cation can  be  deduced  mathematically : 

I  I .  If  it  is  impossible  to  form  a  figure  out  of  the  linear  seg- 
ments corresponding  in  length  to  the  component  weights,  i.e.,  if 
one  segment  is  as  long  or  longer  than  all  the  rest  together,  the 
location  always  lies  in  the  corner  of  this  component.  This  becomes 


evident  by  merely  observing  the  mechanics  of  the  "weights"; 
for  if  the  one  pulling  weight  is  as  great  or  greater  than  all  the  rest 
put  together,  it  cannot  be  moved  by  them  from  its  corner. 

2.  If,  however,  a  weight  figure  can  be  constructed,  i.e.,  if  no 
one  weight  is  as  great  or  greater  than  all  the  rest  together,  the 
locational  figure  becomes  important.  If  the  locational  figure 
is  as  simple  as  a  triangle,  we  can  discover  the  location  by  a 
simple  construction  (cf.  for  the  mathematical  analysis  Appen- 

57  dixl,§4). 

The  general  meaning  of  this  construction  is  that  two  "cor- 
ners of  the  locational  figure"  can  always  be  seen  from  the  loca- 
tion at  an  angle,  the  size  of  which  depends  upon  the  relative  size 
of  the  component  weights  of  these  corners  (in  comparison  with 
the  component  weight  of  the  other  corners).  If  the  relative  size 
is  large,  the  angle  will  be  large;  and  therefore  the  location  lies 
upon  a  lower  arc  connecting  the  two  corners,  thus  being  neces- 
sarily close  to  the  corners.  And  vice  versa,  if  the  relative  com- 
ponent weight  of  the  corners  is  small,  the  angle  will  be  small 
also ;  and  the  location  lies  upon  a  higher  arc  connecting  the  two 
corners.  The  location  will  thus  probably  lie  jar  from  both  cor- 
ners, and  certainly  far  from  the  weaker  of  the  two.  This  de- 
scribes in  exact  terms  how  the  relative  size  of  the  weights  affect 
the  location  with  respect  to  the  position  of  corners. 

There  is  one  more  remark  to  be  made.  The  third  corner  may 
lie  within  the  determining  arc  which  contains  the  other  two,  so 
that  the  determining  arcs  intersect  each  other,  not  within,  but 
outside  of,  the  locational  figure  (see  Figs.  7  and  8).  That  occurs 
either  when  the  component  weights  of  two  corners  in  comparison 
with  the  third  are  small,  and  the  determining  arc  therefore  ex- 
tends very  high  over  them  (Fig.  7),  or  when  the  third  corner 
lies  near  the  connecting  line  of  the  other  two  comers  (Fig.  8). 
In  these  cases  the  location  does  not  move  beyond  this  inclosed 
comer,  but  lies  at  this  corner  as  in  the  first  case  when  the  weight 

58  of  this  comer  entirely  preponderates  (see  Appendix  I,  §7). 


Three  cases  may  be  distinguished  if  the  locational  figure  is 
a  triangle : 

In  the  first  case,  the  weight  appHcable  to  one  comer  is  equal 
to  or  larger  than  the  sum  of  the  other  two  weights ;  then  the  loca- 
tion always  lies  at  this  corner. 

In  the  second  case,  the  weight  applicable  to  the  one  corner 
is  not  equal  to  or  larger  than  the  sum  of  the  other  weights,  but 
it  preponderates  considerably.  If  this  corner  does  not  lie  too  far 
away,  it  is  likewise  the  location.^ 

In  the  third  case,  the  point  where  the  "determining  arcs" 
intersect  is  the  location.  It  lies  near  any  two  corners,  or  far  from 

Fig.  7  Fig.  8 

them,  according  to  the  size  of  their  weights,  compared  with  the 
weight  of  the  third  corner. 

3.  For  all  locational  figures  other  than  triangles,  we  do  not 
have  any  such  simple  method  of  determining  the  location  (see 
Appendix  I,  §12).  The  mechanics  of  the  described  frame  of 
Varignon  offer  the  easiest  way  for  determining  it.  We  can,  how- 
ever, imagine  that  the  location  is  pulled  toward  any  two  corners 
of  a  given  locational  figure  according  to  the  relative  size  of  their 
component  weights,  and  we  can  thus  apply  the  general  idea 
gained  from  the  triangle  to  these  more  complicated  figures;  al- 
though the  pulling  forces  cannot  be  so  easily  expressed  mathe- 
matically as  in  the  case  of  the  triangle.  Although  high  or  low 
arcs  no  longer  afford  a  mathematical  expression  of  the  location 

*  Under  this  case  comes  also  the  instance  of  a  close  geographical  proximity 
of  the  third  corner,  but  this  instance  will  be  disregarded  for  the  present. 


being  pulled  to  any  two  corners,  nevertheless  the  foregoing  fur- 
nishes a  basis  for  a  general  picture  of  where  the  location  lies  in 
these  complicated  figures. 


What  follows  from  these  simple  mathematical  conclusions 
as  regards  reality?  Do  they  cover  reality  completely? 

For  all  cases  in  which  localized  materials  are  employed,  the 
foregoing  obviously  furnishes  a  sufficient  explanation  as  to  where 
the  location  will  lie.  Whether  a  complicated  locational  figure 
results  from  the  employment  of  numerous  materials,  or  whether 
a  simple  triangle  results  from  the  use  of  only  two  materials,  or 
whether  finally  the  employment  of  a  single  material  causes  this 
locational  figure  to  shrink  to  a  ^'line"  which  connects  the  one 
material  deposit  with  the  place  of  consumption,  the  mechanics 
59  will  always  remain  the  same.  The  material  deposits  will  pull 
with  the  weight  of  the  material,  the  place  of  consumption  with 
the  weight  of  the  product,  and  the  location  will  be  determined 
in  the  manner  which  has  been  discussed.  The  determining  me- 
chanics are  simplified,  however,  when  tlie  "figure"  shrinks  into 
a  Hne — the  only  two  existing  components  (that  of  the  one  ma- 
terial deposit  and  that  of  the  place  of  consumption)  coinciding 
and  thus  connecting  the  two  places.  Along  this  straight  hne  the 
weight  of  the  material  will  pull  in  the  one  direction,  the  weight 
of  the  product  in  the  other;  and  the  preponderance  in  weight  of 
the  one  over  the  other  will  determine  where  the  location  lies  upon 
the  line.  This  means  that  the  location  will  be  at  the  "deposit"  in 
case  the  material  has  the  larger  weight,  and  at  the  place  of  con- 
sumption in  case  the  product  has  the  larger  weight.  In  case  the 
weights  are  equal,  the  location  will  be  anywhere  on  the  line. 

When  localized  materials  are  employed,  what  will  be  the  re- 
sult if  ubiquities  like  water  are  used  in  addition?  This  question 
arises  if  any  increase  in  weight  of  the  product  over  and  above  the 
used  weights  of  localized  material  results  from  the  use  of  ubiq- 
uities, as  was  assumed  previously.  The  ubiquities  have  no  defi- 


nite  deposits  which  could  influence  the  locational  figure;  they  are, 
according  to  their  very  definition,  present  everywhere.  Their 
effect  seems  at  first  thought  to  be  altogether  beyond  analysis  by 
locational  figures;  however,  that  is  not  the  case.  Since  they  are 
available  wherever  production  may  take  place,  they  will  in  fact 
be  obtained  wherever  the  location  is,  which  means  that  they  will 
exert  an  influence  upon  the  locational  figure,  not  as  a  material, 
but  only  in  their  manufactured  form  within  the  product.  They 
become  significant  for  locational  purposes  only  because  they  in- 
crease the  weight  of  the  product.  In  other  words,  they  affect  the 
locational  figure  simply  by  strengthening  the  component  of  the 
place  of  consumption  (which  goes  from  the  location  to  the  place 
of  consumption),  because  they  add  to  this  component  their 
weight — a  weight  which  had  not  previously  appeared.  60 

When  we  reflect  upon  this  we  see  that  the  theory  fully  covers 
reality ;  it  covers  the  case  of  both  locaHzed  materials  and  ubiq- 
uities. Evidently  it  should  be  possible  to  develop  out  of  this 
theory  all  variations  of  reality. 


So  far  as  transportation  is  concerned,  we  might  look  upon 
the  process  of  determining  location  as  a  struggle  between  the 
different  corners,  i.e.,  between  the  corner  of  consumption  and  the 
comers  of  the  materials.  What  determines  the  outcom.e  of  this 
struggle?  Perhaps,  one  might  think,  the  extent  to  which  material 
is  used  in  the  manufacture  of  a  product,  and  therefore  the  num- 
ber of  tons  of  material  which  are  required  for  one  ton  of  product. 
Or,  what  would  be  the  same,  the  extent  of  the  losses  of  material, 
productive  processes  with  many  tons  of  material  per  ton  of 
product  being  oriented  near  the  material,  and  other  types  of 
productive  processes  being  oriented  near  the  place  of  consump- 
tion. Judging  from  our  previous  conclusions,  that  is  incorrect. 
The  same  quantity  of  coal  or  other  weight-losing  factors  may  be 


employed  per  ton  of  product  in  two  cases  and  yet  the  two  loca- 
tions may  lie  at  entirely  different  points  in  the  locational  figure; 
indeed,  in  one  case  at  the  place  of  consumption,  in  another  case 
at  the  deposit  or  near  the  deposits.  It  depends  upon  how  strong, 
relatively,  the  component  of  the  place  of  consumption  is — pos- 
sibly as  strenghtened  by  ubiquities. 

The  determining  factor  is  not  the  proportion  of  the  weight 
of  used  material  to  the  weight  of  the  product,  but  the  proportion 
of  the  weight  of  used  localized  material  to  the  weight  of  the  prod; 
uct,  all  ubiquities  being  of  importance  only  as  they  increase  this 
weight  of  the  product.  This  proportion  of  weight  of  localized 
material  to  weight  of  product  we  shall  term  "material  index"  of 
production.  Consequently  a  productive  process  which,  for  ex- 
ample, uses  one  ton  of  localized  material  plus  half  a  ton  of  ubiq- 
uities for  one  ton  of  the  product  has  a  "material  index"  of  one; 
so  also  has  one  which  uses  a  whole  ton  of  ubiquities  in  addition 
6 1  to  one  ton  of  localized  material  (for  example,  a  ton  of  earth  in 
addition  to  one  ton  of  coal);  and  so  also,  of  course,  has  one 
which  uses  simply  one  ton  of  pure  material.  Abstractly  speaking, 
they  are  all  oriented  alike. 

If  we  thus  call  the  proportion  of  the  weight  of  localized  ma- 
terial to  the  weight  of  the  product  the  "material  index"  of  an 
industry,  one  may  say  further:  the  total  weight  per  unit  of  prod- 
uct to  be  considered  for  the  movement  within  the  locational 
figure  in  any  kind  of  productive  process  apparently  depends 
simply  upon  this  material  index  of  the  industry.  For  this  ma- 
terial index  indicates  how  many  weight  units  of  localized  ma- 
terial have  to  be  moved  in  the  locational  figure  in  addition  to  the 
weight  of  the  product.  The  material  index  measures  the  total 
weight  to  be  moved.  This  total  weight  to  be  moved  in  a  loca- 
tional figure  per  unit  of  product  we  shall  from  now  on  call  the 
"locational  weight"  of  the  respective  industry.  It  is  evident  that 
this  locational  weight  has  the  minimum  value  i  when  the  ma- 
terial index  (M.I.)  has  the  value  o  (which  it  would  have  when 


ubiquities  only  had  been  used),  and  rises  parallel  to  the  material 
index:  M.I.  =  y2,  L.W.  =  iVi,  etc. 

We  now  can  state  the  following  conclusions  regarding  the 
struggle  with  respect  to  location  between  the  place  of  consump- 
tion and  the  material  deposits. 

First,  generally  speaking,  industries  having  a  high  locational 
weight  are  attracted  toward  material;  those  having  low  loca- 
tional weight  are  attracted  toward  consumption;  for  the  former 
have  a  high,  the  latter  a  low,  material  index.  In  view  of  our 
mathematical  conclusions,  then,  all  industries  whose  material 
index  is  not  greater  than  one  and  whose  locational  weight  there- 
fore is  not  greater  than  two  lie  at  the  place  of  consumption. 

Second,  with  respect  to  the  composition  of  the  material  index 
we  can  deduce  the  following:  Pure  materials  can  never  bind  pro- 
duction to  their  deposits.  For  since  they  enter  without  loss  of  62 
weight  into  the  product,  the  sum  of  the  component  weights  of 
their  deposits  is  always  at  most  equal  to  the  weight  of  the  prod- 
uct, and  therefore  the  material  index  which  they  create  never  is 
more  than  one.  We  shall  see  the  details  below.  Weight-losing 
materials,  on  the  other  hand,  may  pull  production  to  their  de- 
posits. For  this  to  happen,  however,  it  is  necessary  that  the 
material  index  which  they  codetermine  be  greater  than  one,  and 
that  their  portion  of  the  material  index  be  equal  to  that  of  the 
remainder  plus  the  weight  of  the  product.  Stated  more  simply, 
their  weight  must  be  equal  to  or  greater  than  the  weight  of  the 
product  plus  the  weight  of  the  rest  of  the  localized  materials. 

I  4.  CASES 

Let  us  now  analyze  the  various  possible  cases  of  reality,  and 
let  us  attempt  to  exhaust  all  possible  combinations.  The  follow- 
ing possible  combinations  of  materials  in  the  various  industries 
are  to  be  considered:  (i)  use  of  ubiquities  only,  (2)  use  of  lo- 
calized pure  materials  alone  or  with  ubiquities,  (3)  use  of  weight- 
losing  materials  alone  or  with  other  materials. 


1.  Ubiquities  only. — {a)  One  ubiquity:  In  this  case  pro- 
duction will  always  choose  its  location  at  the  place  of  consump- 
tion. Our  theory  shows  that  the  locational  figure  shrinks  into 
one  ^'point,"  the  place  of  consumption  at  which  production  must 
occur.  It  is  obvious  from  the  facts;  for  if  production  occurs  at 
the  place  of  consumption,  there  is  nothing  at  all  to  be  trans- 
ported, while  any  other  location  would  necessitate  transportation 
after  the  production,  {b)  Several  ubiquities:  There  appears  to 
be  no  reason  why  the  location  should  be  chosen  elsewhere  than 
in  the  case  of  only  one  ubiquity;  the  location  will  lie  at  the  place 
of  consumption. 

2.  Localized  pure  materials  either  alone  or  with  ubiquities. 
63  — a)   If  one  pure  material  is  used  alone,  the  locational  figure 

shrinks  to  a  ''line";  as  mentioned  before,  the  line  from  the  de- 
posit of  the  material  to  the  place  of  consumption.  Along  it  pull 
the  weight  of  the  material  and  the  weight  of  the  product  in  oppo- 
site directions.  In  this  case  the  material  index  is  equal  to  one, , 
since  the  material  enters  in  its  entirety  and  no  further  material  is 
added  and  the  two  weights  are  equal.  The  same  weight  is  to  be 
transported  whether  production  is  carried  on  at  the  place  of  con- 
sumption, at  the  material  deposit,  or  somewhere  in  between. 
The  location  is  mobile;  it  may  lie  at  any  point  along  this  "line" 
or  at  one  of  its  two  termini,  the  place  of  consumption,  or  the 
material  deposit. 

b)  If  ubiquities  are  added  the  location  is  affected.  The  ma- 
terial index  is  less  than  one;  the  component  of  the  material  de- 
posit is  smaller  (just  by  the  ubiquities)  than  that  of  the  place  oi 
consumption;  and  the  location  is  therefore  situated  at  the  latter, 

c)  In  the  case  of  several  pure  materials  alone,  the  material 
index  is  again  equal  to  i.  According  to  our  theory,  therefore, 
the  location  should  be  at  the  place  of  consumption;  for  the  ma- 
terial index  does  not  pull  the  weight  of  the  product  along  one 
line,  but  along  as  many  different  lines  as  there  are  materials.  Nc 
single  one  of  these  components  is  equal  to  the  component  of  the 


place  of  consumption;  the  latter  is  as  large  as  all  of  them  to- 
gether. It  therefore  keeps  the  place  of  production  at  the  place 
of  consumption.  This  may  also  be  established  by  another  Hne  of 
reasoning.  The  weights  of  all  materials,  whether  in  the  form  of 
materials  or  in  the  form  of  product,  have  to  be  moved  from  their 
deposits  to  the  place  of  consumption.  They  should  not  go  out 
of  their  way  unnecessarily;  therefore  each  material  should  re- 
main on  the  straight  Hne  leading  from  its  deposit  to  the  place  of 
consumption.  Unless  the  way  of  one  should  lead  by  chance 
through  the  deposit  of  another,  all  these  ways  will  meet  for  the 
first  time  in  the  place  of  consumption.  Since  their  assembly  at 
one  place  is  the  necessary  first  condition  of  manufacturing  the 
product,  the  place  of  consumption  will  be  the  location.  There- 
fore a  productive  enterprise  using  several  pure  materials  alone 
is  always  located  at  the  place  of  consumption. 

d)  If  ubiquities  are  added  the  location  is  bound  to  the  place 
of  consumption  more  firmly  still.  The  material  index,  which  was 
I  in  case  c,  becomes  less  than  i.  The  component  of  the  place 
of  consumption  is  not  merely  just  as  strong  as  all  the  other  com- 
ponents together;  it  is  stronger.  That  being  true,  it  is  quite  im-  64 
possible  to  separate  the  location  from  the  place  of  consumption. 

3.  Use  of  weight-losing  materials  alone  or  in  connection 
with  other  materials. — (a)  One  weight-losing  material  alone 
gives  us  again  the  one  straight  line  to  which  the  locational  figure 
shrinks.  But  in  this  case  the  location  is  not  mobile,  for  the  com- 
ponent of  the  material  deposit  affecting  location  is  larger  by  the 
loss  in  weight  of  the  material.  The  material  index  is  by  this  loss 
lin  weight  larger  than  i.  Therefore  the  location  is  at  the  deposit. 

b)  But  if  ubiquities  are  added,  they  strengthen  the  compon- 
ent of  the  place  of  consumption  and  the  choice  of  the  location 
depends  upon  the  degree  to  which  they  do  this.  The  location 
^remains  at  the  deposit  as  long  as  the  material  component  remains 
larger,  i.e.,  as  long  as  the  material  index  remains  larger  than  i. 


As  soon  as  the  component  of  the  place  of  consumption  exceeds 
in  weight  (i.e.,  as  soon  as  the  material  index  becomes  less  than 
I ) ,  the  location  moves  to  the  place  of  consumption.  Therefore 
the  choice  of  the  location  is  determined  by  the  comparative  size 
of  the  losses  in  weight  and  of  the  weight  of  the  ubiquities. 

c)  Several  weight-losing  materials  alone  make  impossible  a 
precise  single  statement  concerning  the  position  of  the  location. 
In  such  a  case  the  locational  figures  of  our  theory  become  oper- 
ative. The  general  theorems  we  have  obtained  allow  us  to  say: 
If  weight-losing  materials  alone  enter  into  the  production,  the 

.— _p, 

material  index  is  always  more  than  i,  and  the  location  of  pro- 
duction will  therefore  be  drawn  somehow  towards  the  material 
deposits.  From  our  mathematical  analysis  we  know  by  what 
arcs  running  through  the  material  deposits  the  location  is  deter- 
mined in  the  case  of  two  materials.  We  know  further  that  the 
location  can  lie  at  the  place  of  consumption  only  if  the  latter  lies 
by  chance  within  this  arc;  and  that  the  location  goes  in  every 
instance  (when  two  or  more  materials  exist)  entirely  to  one  de- 
posit, if  the  weight  of  this  one  deposit  is  equal  to  that  of  all  the 
rest  of  the  deposits  plus  the  weight  of  the  product.  This  latter 
fact  enables  us  to  realize  in  what  case  coal,  for  example,  has  the 
power  to  attract  the  location  to  its  deposits ;  it  is  the  case  when 
its  weight  is  equal  to  the  weight  of  the  product  plus  that  of  all 
65  other  localized  materials  employed. 

If  more  than  two  materials  enter,  Varignon's  frame  may  be 
used,  as  we  know.  We  may  visualize  the  geographical  region  at- 
tracting the  location  which  is  created  by  the  preponderance  of 



the  material  index  more  distinctly  by  connecting  the  points  of 
material  deposits  into  one  figure  (Cf.  Fig.  9).  The  triangle  Mi, 
Mo,  Ms  will  be  the  region  attracting  the  location.  Its  force  of  at- 
traction will  be  greater  to  the  degree  that  the  preponderance  of 
the  material  index  is  greater. 

d)  Weight-losing  materials  together  with  pure  materials 
cause  the  material  index  to  become  smaller,  since  the  pure  mate- 
rials appear  again  with  their  entire  weight  in  the  component  of 
consumption.  Therefore  the  tendency  toward  the  material  de- 
posits will  be  lessened.  In  this  case  also  the  location  can  never  be 
at  the  place  of  consumption  unless  the  component  of  consump- 
tion is  strengthened  by  ubiquities.  On  the  contrary,  it  will  al- 
ways be  situated  near  the  deposits  unless  the  place  of  consump- 
tion should  accidentally  lie  upon  the  appropriate  arcs.  The 
deposits  of  pure  material  have  no  attracting  force,  however. 
Therefore  the  figure  of  the  weight-losing  materials  (Fig.  9)  can 
be  used  again  to  see  where  the  geographical  center  of  attraction 
of  the  location  lies  and  how  strongly  it  pulls.^ 

^  This  does  not  seem  correct  in  view  of  what  has  gone  just  before.  To  be 
sure,  the  deposits  of  pure  material  would  not  exert  the  same  kind  of  influence  as 
the  weight-losing  materials.  But  suppose  the  proportion  of  weight  of  the  pure 
materials  were  considerable  in  the  particular  product  and  they  happened  to  He 
between  the  deposits  of  weight-losing  materials  and  the  place  of  consumption, 
hke  this : 

Ai  Bi  Ai  and  A2  are  the  deposits  of  the  weight- 

losing  materials  ai  and  ao', 
.  C        Bi  and  B2  are  the  deposits  of  the  pure 
A2  Bi  materials  bx  and  bz. 

Obviously,  if  the  weight-losing  materials  alone  determined  the  location  of  the  pro- 
luction,  it  would  probably  be  at  the  point  halfway  between  Ai  and  A2  if  we  as- 
sume tti  and  02  to  be  of  equal  weight  as  well  as  of  equal  weight  loss.  But  this 
would  mean  that  bi  and  62  would  have  to  be  transported  all  the  way  back  to  that 
ooint.  Obviously,  then,  the  place  of  production  would  lie  somewhere  upon  the  Hne 
connecting  C  with  the  point  halfway  between  Ax  and  A2.  This  point  would  be 
-vhere  the  sum  of  the  ton-miles  of  weight  losses  fli,  02  would  be  equal  to  the  sum 
)f  the  ton-miles  of  bi,  bt. — Editor. 


e)  If,  finally,  ubiquities  are  added  also  the  locational  effect 
should  be  clear  from  what  has  been  discussed  without  further 
explanation.  The  material  index  will  decrease  exactly  in  propor- 
tion to  the  extent  of  their  use,  and  the  influence  resulting  from 
the  loss  in  weight  of  the  other  materials  will  be  counterbalanced. 
As  soon  as  the  losses  in  weight  are  actually  balanced  by  the 
weight  of  ubiquities,  the  material  index  becomes  equal  to  one  and 
the  location  lies  at  the  place  of  consumption  in  spite  of  the  losses 
in  weight.  Exactly  to  the  extent  to  which  this  condition  is  ap- 
proximated as  a  result  of  adding  ubiquities,  the  attracting  force 
of  the  figure  of  the  material  deposits  will  decrease  and  the  at- 
66  tracting  force  of  the  place  of  consumption  will  increase.  If  we 
wish  to  know  whether  a  productive  enterprise  using  all  these 
different  kinds  of  materials  is  attracted  toward  the  material  de- 
posits or  toward  the  place  of  consumption,  we  have  to  compare 
only  the  loss  in  weight  of  its  localized  materials  with  the  weight 
of  the  ubiquities  which  it  uses.  Accordmg  to  which  weight  is  thej 
greater,  one  or  the  other  attractive  force  is  greater. 

All  this  may  serve  to  make  concrete  the  mathematical  theory  i 
and  to  show  how  it  operates  when  it  is  applied  to  individual  in-' 
stances  and  to  show  that  it  covers  them.  Our  construction  (or,j 
if  the  figure  becomes  too  complicated,  Varignon's  ''frame")! 
affords  us  means  of  determining  exactly  the  location  in  every 
individual  case.    As  the  foregoing  examination  of  individual 
cases  has  shown,  this  construction  and  frame  are,  however,  nec- 
essary only  when  weight-losing  materials  are  used,  because  only 
in  this  case  do  we  get  locational  figures  in  which  the  location  does 
not  lie  at  the  place  of  consumption.  In  all  other  cases  it  is  at  thej 
place  of  consumption  except:   (a)  when  only  one  pure  materialj 
is  used;  in  that  case  the  location  is  mobile  along  the  way  between 
the  material  deposit  and  the  place  of  consumption;   (b)   wherj 
only  one  weight-losing  material  is  used;  in  that  case  the  locatior 
lies  at  the  material  deposit;  (c)   when  ubiquities  are  used  in  ad^ 
dition  to  a  weight-losing  material;  in  that  case  the  location  liesj 



either  at  the  deposit  or  at  the  place  of  consumption,  depending 
upon  the  relationship  between  loss  in  weight  and  the  weight  of 
the  ubiquities. 

All  this  follows  from  applying  the  general  mathematical 
theory  of  minimum  points  to  the  combination  of  facts  which  the 
various  industries  present. 


Up  to  this  time  we  have  confined  our  analysis  to  examples  of 
the  transport  orientation  within  isolated  or  single  locational  fig- 
ures. But  it  is  evident  that  fundamentally  the  same  reasoning 
applies  in  the  case  of  the  orientation  of  an  entire  industry.  For 
after  all  this  orientation  means,  as  far  as  transport  orientation  is 
concerned,  simply  the  co-existence  of  a  larger  or  smaller  number 
of  independent  locational  figures  which  are  formed  by  the  vari- 
ous places  of  consumption  and  the  material  deposit.  Still,  it  is  67 
well  to  take  up  a  few  more  questions. 

A.  First  of  all.  How  do  we  get  the  locational  figures  appro- 
priate to  the  orientation  of  an  entire  industry?  Which  are  the 
most  favorably  located  deposits  for  each  place  of  consumption? 
Are  they  simply  and  in  every  case  those  geographically  nearest 
each  place  of  consumption? 

They  are  in  fact  the  geographically  nearest  deposits,  assum- 
ing a  simple  condition  in  which  no  complicated  locational  figures 
3f  counteracting  forces  are  created.  If  only  one  material  is  used 
t  is  self-evident  that  the  nearest  deposit  will  be  chosen,  whether 
:he  place  of  production  lies  at  the  deposit,  along  the  line  between 
he  deposit  and  the  place  of  consumption,  or  at  the  place  of  con- 
sumption. It  is  self-evident  also  that  the  nearest  deposit  will  be 
ised  if  several  pure  materials  are  employed  either  alone  or  in 
:onnection  with  ubiquities,  because  the  location  will  lie  at  the 
)lace  of  consumption,  and  using  the  nearest  deposit  will  facilitate 
)ringing  the  non-ubiquitous  materials  to  the  location.  And  final- 
y,  it  is  self-evident  that  likewise  the  geographically  nearest  de- 


posit  will  be  chosen  if  weight-losing  material  is  combined  with 
other  materials  without  the  existence  of  a  complicated  locational 
figure — in  other  words,  when  ubiquities  are  added  to  only  one 
such  material.  As  we  know,  the  location  in  this  case  may  be 
either  at  the  deposit  of  that  material  or  at  the  place  of  con- 

But  in  the  case  of  an  actual  locational  figure,  the  deposits 
which  form  the  figure  need  not  necessarily  be  the  deposits  geo- 
graphically nearest  to  the  place  of  consumption.  The  following 
may  serve  as  an  example :  Let  us  assume  that  GM  is  the  deposit 



of  weight-losing  material  in  a  wide  territory  and  without  compe- 
tition. Two  deposits  of  pure  material,  however,  compete  with 
each  other,  and  of  these  RMx  is  nearest  to  the  place  of  consump- 
tion, but  farther  from  GM  than  is  RMo,  as  the  figure  shows.  Let 
the  location  be  near  GM  on  account  of  the  preponderance  of  the 
68  loss  in  weight.  It  is  evident  that  not  RM^,  the  deposit  nearest 
geographically  to  the  place  of  consumption,  but  RMo,  the  deposit 
nearest  geographically  to  GM,  will  be  used  in  the  productive 
process  and  will  therefore  form  the  "figure."  Obviously,  if  thd 
location  lies  near  GM,  pure  material  obtained  from  RM^  wouldi 
have  to  make  a  long  trip  first  down  to  GM  and  then  back  again! 
to  the  place  of  consumption;  while  this  trip  is  saved  if  RM2  is 

Stated  generally,  this  means  that  the  factor  which  deter-i 


mines  whether  a  given  deposit  will  be  used  in  forming  the  loca- 
tional  figures  is  the  index  of  transportation  costs  of  the  figure 
thus  resulting.  The  figure  which  has  the  lowest  index  of  trans- 
portation costs  triumphs  in  the  competitive  struggle,  and  for 
that  reason  is  to  be  looked  upon  theoretically  as  the  one  really 
applicable.  Thus  the  deposit  that  will  be  utilized  is  possibly  not 
at  all  the  one  of  its  kind  geographically  nearest  to  the  place  of 
consumption.  If  the  location  does  not  lie  in  the  vicinity  of  the 
place  of  consumption,  but  rather  in  the  vicinity  of  a  deposit 
(i.e.,  if  the  materials,  or  indeed  one  of  them,  predominates), 
geographical  proximity  to  the  place  of  consumption  will  be  de- 
cisive only  in  the  case  of  this  one  material.  But  in  the  case  of 
the  other  materials,  proximity  to  the  deposit  of  the  predomi- 
nating material  will  be  the  significant  factor  in  determining 
which  particular  deposits  will  be  used  in  the  productive  process, 
and  will  in  consequence  determine  the  locational  figure.  In  those 
modern  industries,  for  example,  in  which  coal  represents  such  a 
predominating  material,  the  geographical  proximity  to  coal  de- 
posits, and  not  to  places  of  consumption,. decides  whether  par- 
ticular deposits  of  the  remaining  materials  will  be  utihzed.  To 
be  sure,  in  these  instances  the  production  will  be  oriented  in  lo- 
cational figures  which  are  formed  by  coal  deposits,  which  are  in 
geographical  proximity  to  the  respective  places  of  consumption; 
but  this  having  been  taken  into  account,  the  locational  figures 
are  formed  by  the  material  deposits  which  are  as  near  as  pos- 
sible these  coal  deposits.  Such  figures  therefore  have  a  narrow 
base  at  the  coal  deposits  and  a  long  point  extending  to  the  places 
of  consumption.  Material  deposits  lying  very  near  the  places  of  69 
consumption  but  far  from  the  coal  deposits  remain  unused. 

It  should  be  clear  theoretically  now  how  these  locational  fig- 
ures are  created  when  numerous  deposits  are  available — as  is 
true  in  practical  Hfe.  The  exact  mathematical  method  to  be  used 
in  determining  these  figures  in  case  the  optimal  deposit  of  one 


material  is  definite  and  a  second  material  is  then  introduced  is 
offered  by  Mathematical  Appendix  I,  §io,  Fig.  52. 

In  Fig.  52  ^1  is  the  place  of  consumption,  A  2  the  deposit  of 
the  one  predominating  material  whose  deposit  is  definite,  A-^ 
(which  is  assumed  to  be  mobile)  representing  the  still  undeter- 
mined deposit  of  the  second  material.  The  lines  of  equal  trans- 
portation costs,  which  are  drawn  for  the  location  figures  arising  \ 
fiom  various  possible  positions  of  A 5,  indicate  which  of  the  sev- 
eral deposits  of  the  second  material  will  actually  be  used  for  the 
locational  figure.  Naturally  that  deposit  will  be  chosen  whose 
use  entails  the  smallest  transportation  costs.  This  will  be  the  de- 
posit within  the  lowest  lines  of  transportation  costs  as  drawn  in  - 

Fig.  52. 

B.  Two  more  aspects  of  the  orientation  of  an  entire  industry 
should  be  mentioned : 

a)  It  is  not  necessarily  the  case  that  but  one  single  place  of  I 
production  exists  for  the  supply  of  every  place  of  consumption. 
Firstly,  it  can  and  will  happen  that  several  locational  figures 
with  equal  or  approximately  equal  transportation  cost  indices 
exist.  If,  for  example,  one  material  lies  nearer  the  place  of  con- 
sumption in  one  locational  figure  while  the  other  material  lies 
nearer  the  place  of  consumption  in  the  other  locational  figure, 
the  two  figures  have  equal  transportation  costs  indices.  This  re- 
sults in  equality  of  competition  and  makes  possible  the  use  of 
the  places  of  production  of  both  figures.  This  might  be  the  out- 
grov/th  of  natural  conditions ;  but  it  may  also  happen  that  an  ap-i 
propriate  tariff  policy  might  equalize  the  transportation  costs 
indices.  Secondly,  and  more  important  still,  it  can  and  will  hap- 
pen that  the  normal  output  of  the  material  deposits  of  the  most 
favorable  locational  figures  may  not  be  sufficient  to  supply  tho 
70  demand  of  the  place  of  consumption.  In  that  case  less  favorable 
locational  figures  appertaining  to  the  use  of  other  material  de- 
posits will  of  course  be  brought  into  play.  As  a  result  large  cen- 
ters of  consumption  (especially  the  modern  metropolis)  will 


often  be  supplied  by  a  multitude  of  places  of  production  which 
belong  to  locational  figures  with  different  transportation  cost  in- 
dices. These  places  will,  as  they  grow,  continuously  bring  to 
life  ''dead  material  deposits,"  and  they  will  bring  into  existence 
new  locational  figures  whose  place  of  consumption  they  repre- 
sent. As  a  result  they  will  create  new  places  of  production. 

b)  Just  as  the  possible  output  of  a  material  deposit  may  be 
smaller  than  is  necessary  for  the  supply  of  the  place  of  consumjv 
tion  to  which  it  belongs  locationally,  so  the  possible  output  may 

Fig.  II 

be  greater,  very  much  greater.  That  will  be  the  case  for  all  ma- 
terials localized  in  large  masses.  The  result  is  that  such  a  mate- 
rial deposit  is  used,  not  only  for  that  first  place  of  consumption, 
i  but  also  for  all  other  places  of  consumption  for  which  it  gives 
'  better  transportation  cost  indices  than  do  other  deposits.  Such 
material  deposits  will  accordingly  appear  as  the  center  of  loca- 
I  tional  figures  grouped  about  them.  If  they  quite  definitely  pre- 
,  dominate  in  attracting  the  location,  these  deposits  will  become 
!  the  center  of  a  production  whose  products  are  distributed  in  all 
directions.  All  this  should  give  a  sufficiently  clear  idea  of  the 
orientation  of  an  entire  industry  so  far  as  transportation  costs 
are  concerned,  not  merely  an  idea  of  the  orientation  of  an  indi- 
vidual plant.  Of  course,  this  is  only  a  theoretical  statement;  how 
the  orientation  of  industry  will  look  in  actual  cases  cannot  be 
stated  abstractly.  The  factors,  however,  upon  which  the  orienta- 


tion  of  an  industry  depends  calls  for  a  discussion  with  a  view  to 
determining  how  they  change  under  the  influence  of  the  actual 
71   development  of  the  economic  system. 


Theoretically  speaking,  the  only  factor  upon  which  the 
choice  of  the  location  of  an  industry  depends,  so  far  as  transpor- 
tation is  concerned,  is  the  material  index  of  the  industry  and  the 
composition  of  that  index.  The  fact  should  be  emphasized  that 
nothing  else  can  determine  or  change  the  fundamental  transpor- 
tational  network  of  orientation  except  this  factor;  and  this  fac- 
tor is  determined  wholly  and  exclusively  by  the  temporary  tech- 
nical situation  in  the  various  branches  of  production.  We  shall 
see  later  how  the  extent  of  the  deviations  from  this  fundamental 
network  (deviations  produced  by  other  causes  or  factors  of  ori- 
entation) is  determined:  first,  by  further  factors  related  to  the 
nature  of  the  various  branches  of  production;  second,  by  gen- 
eral environmental  conditions,  such  as  the  ''density  of  consump- 
tion," the  resulting  "density  of  production"  and  the  existing  gen- 
eral "rate  level"  of  transportation.  In  molding  the  fundamental 
transportational  network  of  industrial  orientation  these  factors 
amount  to  nothing.  The  increasing  "density  of  consumption" 
may  necessitate  the  utilization  of  new  material  deposits  because 
of  the  insufficiency  of  those  already  used ;  it  may  thereby  bring 
into  existence  further  locational  figures  and  places  of  produc- 
tion, and  thus  cause  a  further  evolution  of  the  fundamental  net- 
work. But  the  rise  or  decline  of  the  general  "rate  level"  does 
not  change  anything  at  all  in  the  whole  picture.  It  does  increase 
or  decrease  the  "cost  index"  in  all  locational  figures,  but  it  dis- 
places thereby  neither  the  location  within  these  figures  nor  the 
interacting  conditions  of  their  formation.  Paradoxically,  the 
fundamental  network  of  the  orientation  of  industry,  which  one 
thinks  of  as  being  under  the  exclusive  influence  of  costs  of  trans- 
portation, is  independent  of  the  general  level  of  these  costs. 


In  fact,  however,  the  transportational  orientation  of  indus- 
try which  seems  so  exclusively  determined  by  the  relations  of 
materials  depends,  on  account  of  these  relations,  upon  two  fac- 
tors. These  two  factors  determine  the  "material  index"  of  every 
I  industry  (which  is,  as  we  have  seen,  the  theoretical  expression  of 
1  the  determining  relations  of  the  materials).  One  is  the  size  of 
the  weight  losses  of  localized  materials  during  the  process  of 
production,  and  the  other  is  the  weight  of  the  ubiquities  used.  72 
'  Every  increase  of  the  weight  losses  in  production  increases  the 
material  index;  and  every  increase  of  the  use  of  ubiquities  de- 
creases it,  and  vice  versa.  And  it  is  important  to  observe  that 
these  are  the  07tly  two  things  which  are  able  to  increase  or  de- 
crease the  material  index;  they  therefore  determine  it  and  thus 
settle  the  question  (which  depends  upon  the  material  index) 
whether  an  industry  is  more  attracted  toward  materials  or  to- 
ward consumption.  In  any  given  industrial  process  it  is  the  pro- 
portion of  the  weight  of  the  ubiquities  used  to  the  weight  losses 
of  localized  materials  which  gives  the  basic  answer  to  the  ques- 
tion whether  the  particular  industry  settles  at  the  places  of  con- 
sumption or  moves  to  the  material  deposits. 


What  significance  has  the  foregoing  statement  for  the  devel- 
opment of  transport  orientation?  How  do  these  two  conditions 
change  in  it,  and  with  what  result?  This  is  the  situation:  In 
reaHty,  development  generally  means  in  good  times  a  continual- 
ly increasing  control  of  nature  and  a  continually  progressing 
concentration  of  population.  Development,  thus  defined,  pro- 
duces the  following  changes  in  the  conditions  of  transport  orien- 
tation : 

In  the  first  place,  the  development  will,  as  it  concentrates 
population,  produce  an  ever-increasing  demand  for  the  available 
amount  of  ubiquities.  In  consequence,  unreproducible  ubiqui- 
ties will  be  used  up  at  certain  places,  and  reproducible  ubiquities 


will  be  in  such  demand  at  many  places  that  the  demand  will  ex- 
ceed the  local  output.  In  both  instances  this  will  eliminate  the 
ubiquities  from  the  production  at  these  places;  in  the  first  in- 
stance entirely,  and  in  the  second  instance  for  that  part  of  the 
production  whose  demand  can  no  longer  be  supplied  locally. 
And  this  elimination  of  ubiquities  will,  with  the  progress  of  de- 
velopment and  an  increasing  concentration  of  population,  as- 
sume ever  greater  proportions.  This  process  can,  practically 
speaking,  go  so  far  in  regions  of  concentration  of  population  that 
73  the  manufacturing  of  materials  which  might  in  themselves  (i.e., 
technically)  be  producible  anywhere  becomes  in  fact  a  manufac- 
turing of  materials  which  must  be  obtained  from  other  places, 
(i.e.,  localized  materials).  This  means  that  the  development,  in 
so  far  as  it  signifies  concentration  of  population,  continuously  di- 
minishes the  share  of  ubiquities  in  production  and  substitutes 
localized  materials  in  their  place.  This  constantly  lowers  the 
weights  of  the  components  of  the  place  of  consumption.  This  is 
one  effect  of  the  general  development. 

In  the  second  place,  development,  in  so  far  as  it  signifies  an 
increasing  control  of  nature,  will  influence  the  amount  of  the 
losses  in  weight  of  the  localized  materials  thus  increasingly  used 
in  production.  One  could  describe  what  takes  place  (on  account 
of  the  increasing  control  of  nature)  as  a  continued  further  tran- 
sition from  the  use  of  materials  which  nature  offers  to  man  ready 
for  use — examples  being  wood,  clays,  etc. — to  the  use  of  mate- 
rials, such  as  minerals,  chemical  substances,  etc.,  which  can  be 
wrung  from  nature  only  by  means  of  industrial  processes.  This 
means  that  increasing  losses  in  weight  will  take  place  in  produc- 
tion. For  the  processes  which  yield  the  new  materials  are  ordi- 
narily burning  processes,  and  therefore,  as  a  result  of  the  use  of 
fuel  material,  they  are  processes  of  considerable  weight  losses. 
Moreover,  the  new  materials  themselves,  because  they  must  be 
isolated,  entail  heavy  losses  in  weight  and  leave  behind  "resi- 
dues" which  are  on  the  average  greater  than  the  residues  of  the 


old  materials  like  wood,  clay,  etc.  Consequently  the  more  such 
new  materials  enter  into  production  the  more  losses  in  weight 
will  be  incurred  by  the  ''materials"  used  in  that  production.  Fur- 
thermore, the  control  of  nature  leads  quite  generally  to  "mech- 
anization" of  production.  Since  this  involves  the  use  of  fuel  ma- 
terial, it  results  in  transforming  every  mechanized  process  into 
a  ''process  of  weight  loss,"  and  in  generally  increasing  the  losses 
in  weight.  The  development  thus  increases  greatly  and  in  many 
ways  the  weight  losses  in  production,  and  therefore  it  tremen- 
dously strengthens  the  material  components  in  addition  to  weak- 
ening the  components  of  the  place  of  consumption  by  displacing 
the  ubiquities.  74 

In  consequence,  industry  must  shift  decidedly  and  continu- 
ally from  the  places  of  consumption  toward  the  material  de- 
posits. And  in  fact  this  view  of  the  general  development  enables 
us  to  understand  the  fundamental  features  of  the  large  indus- 
trial revolution  which  we  have  witnessed  during  the  nineteenth 
century.  The  rapid  concentration  of  population  and  the  rapid 
technical  development  with  its  mechanization  of  production  and 
its  transition  to  the  use  of  metal  both  tended  to  destroy  (and 
just  as  rapidly  as  they  took  place)  the  condition  which  had  pre- 
vailed up  to  that  time,  the  condition  that  industrial  location,  in 
so  far  as  it  was  determined  by  transportation,  coincided  with  the 
places  of  consumption.  This  removal  of  the  location  of  indus- 
trial production  from  the  places  of  consumption  implied  the  de- 
struction of  the  crafts,  for  the  crafts  presupposed  that  industrial 
location  and  the  place  of  consumption  coincided.  Here  we  have, 
as  far  as  locational  theory  is  concerned,  a  general  basis  for  un- 
derstanding the  inevitable  collapse  of  this  kind  of  industrial  or- 
ganization. Of  course  the  crafts  were  undermined  by  many  dif- 
ferent forces,  almost  all  of  them  strong.  It  is  certain  that  the 
change  of  locational  conditions  which  has  been  pointed  out  was 
not  the  weakest  of  these  forces. 



Let  US  now,  for  the  completion  of  our  theory,  leave  the  ab- 
stractions with  which  we  have  been  working  up  to  this  time  and 
modify  our  conclusions  in  order  to  fit  them  into  reality.  We  have 
to  abandon  two  assumptions.  The  first  is  the  assumption  that 
weight  and  distance  are  the  only  factors  that  determine  the  costs 
of  transportation.  This  was  the  fundamental  assumption  of  our 
entire  discussion;  upon  this  theoretical  basis  the  locational  fig- 
75  ures  and  the  positions  of  location  were  worked  out.  The  second 
assumption  was  that  costs  of  transportation,  however  they  mayij 
be  determined  in  individual  instances,  are  always  uniformly  fori 
a  whole  country  those  of  a  single  method  of  transportation.  Thisi 
second  assumption  accompanied  the  first  one  in  all  our  discus- 
sions.  Stated  positively,  these  two  assumptions  mean  that  in 
order  to  fit  our  theory  into  reahty  we  have  to  consider,  first,  the 
existing  system  of  transportation  rates,  and  second,  the  inter-j 
action  of  several  transportation  systems. 


We  have  already  discussed  in  Section  I  (pp.  43  ff.)  how  the« 
deviations  of  the  actual  rate  structure  from  the  theoretical  cal- 
culation of  rates  according  to  weight  and  mileage  may  neverthe- 
less be  expressed  in  terms  of  these  two  elements,  weight  and* 
mileage.  We  saw  that  deviations  which  increase  or  decrease  thet 
mileage  rate  (that  is,  deviations  which  produce  increased  or  de- 
creased rates  for  certain  kinds  of  way,  individual  lines,  or  cer- 
tain distances)  are  capable  of  being  expressed  as  additions  or 
subtractions  of  mileage.  We  also  saw  that  deviations  which  are 
variations  from  the  pure  calculation  of  rates  according  to  weight 
(that  is,  deviations  which  produce  increased  or  decreased  rates 
for  certain  kinds  of  goods)  are  capable  of  being  expressed  as  in- 
creases or  decreases  in  weight,  as  ''fictitious"  additions  or  sub-' 
tractions  of  weight;  this  being  true  whether  they  affect  the  vari- 


ous  kinds  of  goods  generally,  or  only  under  certain  conditions. 
That  was  the  theoretical  solution/^ 

The  next  question  is  what  significance  these  modifications 
have  for  the  structure  of  the  transport  orientations.  How  does   76 
it  change  the  locational  figures,  and  how  does  it  influence  the 
position  of  the  locations  in  these  figures? 

a)  The  deviations  from  the  pure  calculation  of  rates  ac- 
cording to  mileage. — If  certain  lines  are  shortened  in  mileage  by 
special  lower  rates,  or  if  long  distances  are  shortened  in  general 
by  means  of  a  decreasing  scale,  it  evidently  changes  the  relation- 
ship of  the  various  points  to  one  another,  as  they  are  considered 
for  the  locational  figures.  Viewed  from  the  places  of  consump- 
tion, certain  material  deposits  may  be  for  locational  purposes 
closer  or  closer  together  than  would  be  the  case  in  terms  of  their 
actual  geographical  position.  Viewed  from  the  material  deposits, 
a  similar  situation  may  seem  to  obtain.  Since  the  distance  of  the 
material  deposits  from  the  places  of  consumption  and  from  one 
another  determines,  in  terms  of  the  lowest  transportation  cost 
index  (cf.  above,  p.  67),  what  locational  figure  will  be  created, 
these  rate  variations  alter  the  competitive  relationships  of  the 
material  deposits  supplying  the  places  of  consumption,  and  con- 
sequently the  locational  figures  change.  Certain  material  depos- 
its which  would  otherwise  not  be  used  for  forming  the  locational 
figures  of  certain  places  of  consumption  will  now  be  used;  and 
Dthers,  which  would  otherwise  be  used,  will  now  be  eliminated. 
En  this  way,  in  fact,  entirely  different  locational  figures  and 
places  of  production  may  be  created  for  the  supply  of  the  places 
Df  consumption  than  those  we  should  assume,  considering  mere- 
ly the  geographical  locations.  Within  the  locational  figures,  how- 
ever, the  locations  of  production  will  be  determined  exactly  in 
iccordance  with  the  rules  previously  indicated.  Expressed  dif- 
erently,  the  theoretical  position  of  the  location  in  relation  to  the 
naterial  deposits  and  the  place  of  consumption  will  not  be 

'"  Cf .  p.  46  f.,  above. 


changed  at  all;  only  the  locational  figures  within  which  the  loca- 
tion is  determined  will  be  changed.  Looking  at  the  map,  one  will 
perhaps  be  surprised  that  this  or  that  location  has  not  used  an- 
other deposit  which  lies  nearer  geographically.  One  will  find  no 
deviation,  however,  from  the  general  rules  determining  location 
when  the  material  deposits  actually  chosen  are  used  in  the  cal- 
77  culations. 

b)   Deviation  from  the  pure  calculation  of  rates  according 
to  weight. — Evidently  the  commodity  which  enters  into  the  loca- 
tional balance  with  added  or  subtracted  weight  influences  the^ 
locational  balance  with  another  than  its  real  weight;  it  attracts 
the  location  either  more  or  less  than  its  real  weight  would  enable' 
it.  If  a  proportional  addition  or  subtraction  of  weight  does  noti 
take  place  in  the  case  of  all  the  materials,  and  also  of  the  prod- 
uct, and  therefore  does  not  alter  proportionally  the  attracting' 
forces  of  all  corners  of  the  figure,  a  displacement  of  the  location 
will  result  within  the  locational  figure,  the  location  being  at- 
tracted in  the  direction  of  those  corners  which  have  a  propor- 
tionally increased  force. 

If,  for  example,  the  industrial  product  is  bulky,  such  as: 
chairs,  vats,  or  casks,  and  if  materials  used  in  its  manufacture! 
are  not  as  bulky,  the  attracting  force  of  the  component  of  the| 
place  of  consumption  will  be  one  and  one-half  times  the  weight' 
of  the  product,  according  to  the  German  rates.  The  attracting 
force  of  the  place  of  consumption  will,  in  other  words,  be  nol 
merely  the  sum  of  the  weights  of  materials  used,  as  the  pure  the^ 
ory  would  suggest,  but  one  and  one-half  times  that  sum.  It  mayl 
thus  happen  that  the  location  which,  if  the  goods  had  not  beeni 
bulky,  would  have  come  to  lie  somewhere  between  the  material! 
deposit  and  the  place  of  consumption,  will  lie  at  the  place  of  con^i 
sumption  now  that  the  weight  of  the  product  is  in  effect  onei 
and  one-half  times  as  large  as  the  sum  of  weights  of  the  materialjj 
This  is  certainly  in  reality  not  a  rare  occurrence  in  the  case  oi 



bulky  goods.  Similarly,  a  raw  material,  which  is  bulky  (wool) 
but  whose  product  (yarn)  is  not  bulky,  may,  of  course,  pull  the 
location  to  its  material  deposit  or  to  the  vicinity  of  that  deposit. 
The  same  reasoning  applies  to  combustible  goods. 

We  find  a  corresponding,  though  reverse,  effect  when  rates 
are  reduced  on  goods  of  small  value  per  unit  of  weight.  Such  re- 
duced rates  will  almost  always  be  in  effect  subtractions  from  the 
weight  of  materials,  while  they  leave  the  products  untouched  ex- 
cept for  occasional  small  reductions;  for  the  products  have  a  78 
higher  value  than  the  materials.  Reduced  rates  on  goods  of 
small  value  will  therefore  almost  always  mean  reduced  attract- 
ing force  along  the  components  of  the  material  deposits  as  com- 
pared with  that  of  the  place  of  consumption,  and  consequently 
the  location  shifts  toward  the  place  of  consumption.  If,  for  ex- 
ample, in  Germany  almost  all  raw  materials  of  very  small  value, 
such  as  clay,  ore,  and  wood,  are  transported  at  rates  reduced  as 
much  as  60  per  cent,  and  coal  at  rates  reduced  56  per  cent,  it 
surely  means  a  strong  tendency  to  shift  the  location  away  from 
the  material  and  coal  deposits  toward  the  places  of  consump- 
tion." Such  low  rates,  therefore,  constitute  an  attempt  to  dis- 
tribute or  decentralize  the  locations  of  production.  Our  theory 
explains  to  what  extent  this  distributing  measure  will  succeed, 
and  to  what  points  the  locations  of  different  industries  will  be 
shifted.  For  the  locational  figures  we  need  simply  to  ascribe  to 
such  goods  as  are  transported  at  reduced  rates  a  weight  which  is 
reduced  correspondingly.  When  we  construct  the  locational  fig- 
ures we  can  then  calculate  exactly  where  the  transportation 
costs  will  pull  the  locations  as  simply  as  in  the  case  when  no  such 
reductions  are  made.  Whatever  alterations  are  thus  created  by 
reducing  or  increasing  the  rates  of  certain  types  of  goods,  they 
constitute  important  but  exactly  determinable  shiftings  of  the 
ocation  within  the  locational  figure.  It  is  to  be  noted,  however, 

"  The  situation  in  the  United  States  is  similar. — Editor. 


that  this  is  their  only  effect.  A  change  of  material  deposits  does 
not  take  place,  since  such  special  rates  will  always  affect  all  de- 
posits of  the  same  material  to  an  equal  degree,  but  not  the  mile 
age.  Only  a  change  of  these  distances  can  change  the  competi- 
tive advantage  of  various  deposits  and  thus  alter  their  use  within 
the  locational  figures.   In  distinct  contrast  with  the  first  case 
(see  p.  76),  which  changed  the  locational  figures  themselves, 
these  locational  figures  now  under  consideration  remain  un- 
touched by  rate  reductions  on  certain  goods,  and  untouched  also 
on  the  whole  structural  foundations  of  the  orientation  of  pro 
duction;  only  the  locations  themselves  shift  upon  these  founda 
79  tions. 

The  increased  rates  for  shipments  in  small  quantities  (less 
than  carloads  and  piece-goods  shipments)  ought  to  be  mentioned 
specially.  These  rate  increases  may  theoretically  be  expressed 
as  weight  additions.  They  do  not,  however,  concern  certain  defi- 
nite kinds  of  goods;  they  concern  all  goods,  whenever  shipped 
in  such  quantities.  They  seem  to  create  no  factors  which  can  be- 
calculated  precisely  and  generally  when  determining  the  loca 
tion,  since  we  cannot  know  whether  the  production  of  a  giver | 
product  will  or  will  not  attain  the  quantity  which  is  necessary 
for  the  normal  rates  to  become  effective,  and  whether  transpor- 
tation will  or  will  not  have  to  take  place  at  the  increased  rates 
The  distortions  of  the  ^'theoretical"  locational  picture  which  an 
thus  brought  about  seem  not  to  yield  to  general  statements,  al) 
though  they  can  be  calculated  precisely  in  every  individual  casfj 
and  for  every  locational  figure.  We  may  simply  ignore  these  dis 
tortious  for  the  present,  for  every  locational  figure  has  obviouslj 
a  definite  capacity  for  moving  masses  within  it,  which  capacitj 
is  determined  by  the  size  of  its  place  of  consumption.  In  one  lo- 
cational figure,  full  carloads,  in  another  only  less  than  carloac 
shipments,  will  be  moved.  In  the  one  locational  figure  transpor* 
tation,  and  therefore  production  and  consumption,  will  be  cheap 
er  than  in  the  other;  but  this  will  influence  neither  the  figures 



themselves  nor  the  position  of  the  location  within  them.  Accord- 
ingly this  modification  of  the  pure  calculation  according  to 
weight  may  as  a  practical  matter  be  omitted  from  our  consider- 


Our  theory  has  thus  far  assumed  the  system  of  transporta- 
tion to  be  uniform  for  the  whole  territory  considered.  This  does 
not  need  to  be  the  case;  any  existing  system  may  be  divided  into 
independent  parts.  The  theory  has  also  assumed  the  system  of 
transportation  to  be  of  one  kind.  This  is  in  reality  not  the  case; 
there  are  railways,  waterways,  and  highways.  In  applying  our 
theory  to  reality  we  are  confronted  with  the  problem  of  deter- 
mining the  importance  of  these  differences. 


A  few  words  will  suffice  to  discuss  the  possible  division  of 
the  transportation  system  into  parts  which,  although  co-operat- 
ing technically,  operate  as  economically  independent  units.  If 
such  division  results  in  independent  rate-making  by  the  various 
parts  (and  only  in  such  event,  of  course,  is  it  important  for 
transportation  costs)  it  may  be  expedient  to  treat  each  region 
(with  its  different  rates)  simply  as  a  separate  territory  within 
Arhich  industry  orients  itself.  The  decision  whether  or  not  to  do 

'^  This  modification  becomes  important   when  the   production  of  several 
.  ocational  figures  is  "coupled"  by  agglomeration  with  one  another.  In  the  result- 
ng  combined  figures  the  si2e  of  a  single  place  of  consumption  no  longer  deter- 
mines the  possible  amount  of  commodities  moved;  and  therefore  the  rate.   The 
hipping  of  materials  to  the  "places  of  the  combined  production"  may  be  done 
1  carloads  and  therefore  at  cheap  rates,  although  the  capacity  of  the  individual 
laces  of  consumption  only  admits  of  shipments  in  smaller  quantities,  and  there- 
Dre  at  higher  rates.  This  condition  will  have  the  same  effect  as  an  "addition  in 
eight"  to  the  products,  and  therefore  it  means  a  strengthening  of  the  compo- 
ents  of  places  of  consumption.  It  would  perforce  have  in  itself  the  tendency  to 
lift  the  combined  location  toward  the  places  of  consumption ;  if  not,  other  shift- 
igs  would  take  place  in  the  case  of  such  combined  locations — all  of  which  makes 
seem  inadvisable  to  analyze  this  tendency  further  at  this  juncture  (cf.  injra, 
3.  i34ff.). 



so  will  depend  upon  the  extent  of  the  differences  in  the  rates.  It 
would  be  expedient  to  do  so,  for  example,  when  very  many  addi- 
tions and  subtractions  from  the  normal  rates  are  made  in  the  dif- 
ferent regions.  In  this  case  a  considerably  different  "theoretical" 
distinction  of  the  locations  would  prevail  in  each  of  the  regions, 
and  it  would  be  better,  therefore,  to  consider  them  independ- 

On  the  other  hand,  we  may  treat  the  rate  variations  as  local 
modifications  of  a  uniform  system  of  rate-making  in  a  uniform 
territory  of  orientation.  To  do  so  will  be  possible  and  expedient  I 
only  when  nothing  but  the  rates  of  some  unimportant  goods  vary- 
from  one  territory  to  another.  This  situation  exists,  for  example, 
with  regard  to  the  system  of  rates  within  the  German  Common- 
wealth, and  this  fact  makes  it  possible  for  us  to  treat  the  entire 
German  territory  as  uniform,  as  far  as  the  orientation  of  indus- 
try is  concerned. 


When  different  kinds  of  transportation  systems  work  to- 
gether, more  complicated  problems  seem  to  confront  us.  Bui 
they  only  seem  to  do  so.  If  we  consider  the  situation  as  it  is  to- 
day the  problems  may  be  solved. 

If  we  look  at  the  railway  system,  it  appears  to  be  a  net  which 
may  be  illustrated  by  the  diagram  in  Figure  13.  Within  thisi 
net  the  existing  places  of  consumption  and  the  deposits  of  mate) 
rial  are  located  at  certain  points  as  indicated  in  the  diagram  j 
This  net  has  been  created  in  order  to  connect  these  centers  witij 
one  another.  It  connects  them,  however,  not  by  straight  lines 
but  by  lines  having  many  curves,  the  curves  being  caused  by  thc( 
presence  of  other  centers  and  by  geographical  conditions.  Th<i 
relation  of  the  mathematically  straight  connections  of  the  idea 
locational  figures  to  the  actual  connections  may  be  somewha 
like  those  indicated  in  the  diagram.  The  actual  transportatioi 
depends  upon  the  actual  connections,  although  it  may  be  pos^ 


sible  to  suggest,  and  even  to  bring  about,  certain  improvements 
in  the  actual  connections  as  a  result  of  studying  the  require- 
ments of  the  locational  figures.  Anyway,  the  mathematical  lines 
connecting  the  deposits  of  material  with  the  place  of  production 
and  the  latter  with  the  place  of  consumption  will  in  a  real  case 
appear  only  as  curves;  that  is  self-evident.  Has  that  fact  any 
significance  for  the  application  of  our  rules?    The  answer  is: 

Fig.  13 

Yes,  in  so  far  as  the  choice  of  a  location  can  only  be  an  approx- 
imation of  the  ideal  location  because  the  actual  location  is  im- 
bedded into  a  curved  network  of  transportation.  Among  the  lo-  82 
cational  points  which  may  in  fact  be  considered  in  view  of  the 
presence  of  the  network  of  transportation,  that  point  will  be 
:hosen  which  corresponds  most  closely  to  the  conditions  of  the 
ideal  location.   As  is  indicated  in  the  diagram,  several  of  the 
ictual  points  near  the  ideal  location  may  be  considered.  One  of 
hem,  however  (P'),  will  be  chosen;  because  it,  although  lying 
geographically  farther  away  from  the  ideal  point,  corresponds 
oest  with  the  ideal  requirements  so  far  as  its  position  in  relation 
0  the  material  deposits  and  the  place  of  consumption  is  con- 

Having  set  forth  this  "deforming"  effect  of  reality,  we  shall 
)roceed  to  examine  how  several  kinds  of  transportation  systems 
v^ork  together. 


a)   The  effect  of  the  waterways. — Today  railways  and  high- 
ways work  together.  If  we  treat  the  railway  system  as  the  nor- 
mal system  from  which  we  start  in  our  analysis,  we  find  water- 
ways a  somewhat  cheaper  system  and  highways  a  considerably 
dearer  system.  What,  with  reference  to  location,  is  the  signif- 
icance of  competing  waterways  whose  rates  are  today  in  Ger- 
many something  like  half  the  lowest  railway  rates,  or  about  0.25 
cents  per  ton-mile?  Let  us  reflect  how  waterways  and  railways 
are  related  today  geographically.   Ever3rwhere  we  find  an  ex- 
tremely dense  railway  net  spanning  the  entire  country,  and  wind- 
ing through  this  net  like  ribbons,  some  natural  or  artificial  wa- 
terways. These  may  be  connected  so  as  to  form  a  ''network"  ori 
they  may  be  large  unconnected  rivers.  But  even  in  the  case  of  a; 
network  they  form  a  skeleton  of  such  irregularity  that  they  can- 
not open  up  all  material  deposits  of  the  country,  and  even  less; 
can  they  supply  all  its  places  of  consumption.  As  transportation! 
devices  connecting  cheaply  only  certain  points,  they  thus  tra- 
verse the  railway  system  which  does  open  up  all  material  de- 
posits and  does  supply  all  places  of  consumption,  and  therefore 
actually  carries  the  orientation  of  industry.  Along  the  railways 
the  largest  part  of  the  places  of  production  and  of  the  materia»! 
^2>  deposits  of  the  country  are  situated.  The  railway  net  contaimi 
therefore  the  attracting  points  upon  which  the  locational  figure«! 
and  the  fundamental  outline  of  the  orientation  of  industry  de  j 
pend.  The  waterways  which  traverse  the  railway  system  are  i 
effect  nothing  but  routes  with  especially  cheap  shipping  oppoi 
tunities;  they  may  and  will  be  considered  as  parts  of  the  railwaj 
system  with  especially  low  rates.  Thus  they  are  theoretical!) 
fitted  into  the  concept  of  a  single  and  uniform  system  of  trans 
portation,  and  consequently  into  our  theory.  For  within  such  i 
system,  routes  with  cheaper  rates  mean  nothing  but  distanceii 
shortened  in  proportion  to  the  decrease  in  rates.  In  forming  thfj 
locational  figures,  material  deposits  which  can  use  these  short' 
ened  routes  will  have  an  advantage  over  other  deposits  whicl- 




cannot  use  them.  The  sphere  of  action  of  certain  material  de- 
posits will  be  enlarged;  other  deposits  will  be  eliminated;  and 
certain  locations  will  be  transferred:  these  are  the  effects  of  the 
competition  of  waterways  with  railways.  If  we  know  the  rates 
of  existing  waterways  under  discussion  it  is  not  difficult  to  put 
them  as  locational  elements  into  our  analysis  and  to  determine 
the  resulting  locational  figure  according  to  our  rules.  We  can 


Fig.  14 

Fig.  15 

make  clear  their  influence  by  the  diagrams  as  shown  in  Figures 
14  and  15. 

Case  I :  Elimination  of  a  deposit  of  material  and  addition 
of  another  through  the  influence  of  a  waterway,  transfer  of  the 
locational  figure  and  of  the  location  (compare  Fig.  14). 

The  deposit  M2  is  considerably  nearer  the  place  of  consump- 
tion C  than  the  deposit  M\.  If  no  waterway  existed,  the  loca- 
tional triangle  with  the  place  of  production  P  would  be  formed 
for  the  supply  of  C.  The  existence  of  the  waterway  may,  how- 
ever, cause  the  distance  separating  M'2  from  C  to  become  eco- 
lomically  shorter  than  the  distance  separating  M2  from  C.  In  84 
hat  case  the  locational  triangle  using  M\  and  the  place  of  pro- 
iuction  P'  will  come  into  effect. 



Case  2 :  Naturally,  the  effect  is  not  necessarily  so  far-reach- 
ing; it  is  possible  that  no  change  in  the  utilization  of  the  mate- 
rial deposits  is  brought  about.  In  that  case  the  locational  figure 
remains  the  same,  and  only  a  displacement  of  the  place  of  pro- 
duction takes  place.  Figure  15  will  illustrate  this  smaller  effect. 

Here  also  Mo  lies  nearer  the  place  of  consumption  than  M\, 
but  the  locational  triangle  M^M^C  permits  the  use  of  the  wa- 
terway. The  location  P'  (which  was  chosen  with  a  view  to  using 
this  waterway)  should  therefore  have  a  smaller  index  of  trans- 
85  portation  costs  than  the  location  in  the  triangle  MxM'o  C.  There- 
fore Mo  will  not  be  eliminated,  and  the  locational  triangle  with 
the  material  deposits  it  employed  will  remain  the  same  as  if 
there  were  no  waterway.  However,  the  location  will  be  reahzed 
in  P',  and  not  in  P,  which  is  the  most  desirable  location  if  merely 
roads  are  used. 

These  remarks  will  suffice  to  make  clear  the  greater  or  lessi 
effect  of  the  waterways,  and  at  the  same  time  to  show  why  thai 
waterways  are  fringed  with  places  of  industrial  production.  Allj 
these  locations  have,  during  the  process  of  their  becoming  estabn 
Hshed,  received  a  little  jolt  from  the  waterways  which  pushed 
their  position  to  the  right  or  to  the  left.  Although  they  now  have 
their  chimneys  smoking  by  the  water  side,  they  belonged  some 
where  in  the  "neighborhood,"  even  if  there  had  been  only  trans- 
portation by  land. 

b)  The  effect  of  the  net  of  highways. — It  is  well  known  thai 
the  costs  of  transportation  on  the  highway  are  on  the  average 
four  to  ten  times,  and  in  individual  cases  twenty  times,  those  of 
the  railway.^^  As  a  result,  freight  transportation  on  the  high^ 
ways  over  long  distances  has  ceased.  Today  highways  are  used 
only  for  transporting  goods  to  and  from  the  railway  stations^ 
Consequently  highways  no  longer  have  any  independent  loca- 

"  These  sentences  were  written  before  the  advent  of  the  truck,  but  the  stUn 
dent  of  this  treatise  will  find  it  possible  to  work  out  the  problems  created  by  it 
if  he  will  use  the  methods  set  forth  herein. — Editor. 


tional  signficance  at  all;  their  function  is  rather  that  of  a  sub- 
sidiary of  the  railway  system.  If  we  wish  to  understand  the  im- 
portance of  this  subsidiary,  we  had  best  consider  each  district  of 
collection  and  distribution  grouped  around  a  railway  station  as 
a  unit  with  the  railway  station  as  its  center.  As  such  a  unit  the 
district,  whether  a  material  deposit  or  a  place  of  consumption, 
enters  into  the  total  industrial  orientation  through  its  railway 
station.  We  can  disregard  for  the  moment  how  the  district  is  or- 
ganized internally  under  the  influence  of  its  street  system;  this 
is  a  locational  problem  similar  to  that  which  asks  how  industry 
is  grouped  in  a  metropolis  under  the  influence  of  the  traffic  fac- 
tors present  there;  it  is  a  question  of  local  agglomeration  and 
distribution  which  will  be  treated  in  a  later  chapter.  If  such  a  86 
railway  station  unit  (Bahnplatzeinheit) ,  as  I  should  like  to  call 
it,  enters  as  a  material  deposit  into  the  industrial  orientation, 
then  not  the  price  at  the  deposit,  but  the  price  at  the  railway  sta- 
tion, must  be  regarded  as  the  delivery  price  of  the  materials 
(price  at  the  deposit  plus  freight  charges  of  road  carriage) .  For 
obviously  it  is  only  on  the  basis  of  this  price  that  the  material 
deposit  enters  effectively  into  the  orientation  of  industry. 

The  particular  significance  of  differences  in  the  delivery 
prices  will  be  discussed  in  the  next  section.  It  may  be,  of  course, 
(and  very  often  is  the  case)  that  the  material  deposit  and  the 
place  of  consumption  are  so  situated  that  they  do  not  at  all  need 
the  railway,  since  they  are  in  the  same  ''railway  station  unit." 
This  means,  for  the  orientation  of  industry  at  large,  that  they 
are  located  at  the  same  place,  and  therefore  do  not  come  within 
the  scope  of  our  broader  theoretical  considerations.  However, 
for  the  local  orientation  within  the  railway  station  unit,  with  its 
street  net  system,  exactly  the  same  rules  of  orientation  will  be 
operative  in  detail  which  determine  the  orientation  at  large  for 
the  whole  country,  with  its  extensive  transportation  system. 
Everything  will  simply  be  repeated  in  miniature. 




It  has  become  possible  now,  in  closing,  to  abandon  several 
other  important  simplifying  assumptions  and  to  consider  the  im- 
portance of  certain  peculiarities  of  reality  which  have  been 
ignored  until  now.  These  are,  first,  the  price  differences  of  the 
materials  caused  by  the  local  position  of  the  material  deposits 
and  the  railway  stations;  and  second,  the  effect  of  water  power 
87  upon  the  process  of  production.  We  had  said  that  price  differ- 
ences of  the  materials  (which  price  differences  ordinarily  would 
be  an  independent  regional  factor  of  orientation)  may  be  ex- 
pressed theoretically  as  differences  of  transportation  costs  of  the 
materials,  and  thus  may  be  fitted  into  theory.  We  had  said,  too, 
that  water  power  may  be  theoretically  considered  to  be  a  cheap 
fuel;  therefore  it  may  be  expressed  in  price  differences  of  the 
material,  and  thus  likewise  be  fitted  into  the  theory.  Some  very 
important  peculiarities  appear,  however,  when  water  power  en- 
ters in.  Also  the  way  in  which  differences  in  the  prices  of  mate- 
rials may  be  expressed  as  differences  in  the  transportation  costs, 
and  the  way  in  which  they  then  affect  orientation,  need  further 
exemplification.  In  this  exemplification  we  shall  employ  the  lo- 
cational  rules  which  we  have  already  discovered. 


It  does  not  concern  us  here  from  what  cause  price  differences 
of  the  materials  result;  they  may  be  due  to  differences  in  the 
costs  of  production,  or  due  to  artificial  price  fixing,  or  due  to  dif- 
ferences in  the  cost  of  transporting  the  goods  to  the  point  where 
the  materials  enter  the  larger  traffic  (i.e.,  traffic  by  rail  or  by 
water).  We  shall  consider  this  point  as  the  ''deposit"  to  be  used 
in  analyzing  the  large  locational  system,  and  we  shall  calculate 
upon  the  basis  of  the  price  at  this  point. 

Price  differences  themselves  never  change  the  location  with- 
in the  locational  figure  fundamentally;  they  merely  shift  the 
competitive  conditions  among  material  deposits  which  are  equal 


in  other  respects.  Material  deposits  with  low  prices  will  simply 
have  larger  spheres  of  action  than  appears  from  the  geographical 
situation  itself;  they,  rather  than  deposits  more  favorably  situ- 
ated geographically,  will  be  used  to  supply  certain  places  of  con- 
sumption. In  brief,  they  will  operate  in  the  same  way  as  the  88 
change  of  competition  of  material  deposits  caused  by  cheap 
rates  for  certain  Hues  which  was  discussed  earlier. 


Water  power  may  be  used  today  as  a  source  of  power  for 
production  in  two  different  forms:  directly,  under  waterfalls,  or 
indirectly,  through  electrical  transmission.  Both  cases,  as  for- 
mer discussions  have  already  shown,  are  to  be  treated  theoreti- 
cally as  fuel  deposits  with  definite,  and  on  the  whole  with  lower, 
prices.  The  horse-power  which  they  produce  may  easily  be  cal- 
culated in  equivalent  quantities  of  coal,  and  we  may  then  com- 
pare the  weight  of  this  "white"  coal  and  its  price  with  the  quan- 
tities of  ''black"  coal  which  it  replaces.  This  point  is  simple. 
There  exist,  however,  peculiarities  in  the  locational  effect  of 
these  calculated  amounts  of  coal  which  have  to  be  considered 

a)  In  the  case  of  the  use  of  waterfalls,  the  calculated 
amounts  of  coal  can  be  used  only  at  one  place,  at  the  waterfall. 
Locationally,  such  waterfalls  exert  an  alternative  locational  ef- 
fect; either  the  location  goes  to  the  place  of  this  locational  ad- 
vantage, or  it  remains  where  it  is,  and  in  that  event  it  is  abso- 
lutely untouched  by  this  locational  advantage.  When  does  the 
one  thing  take  place,  and  when  the  other?  If  nowadays  the  lo- 
cations remain  untouched  by  this  locational  advantage  it  means, 
practically  speaking,  the  forming  of  locational  figures  and  the 
selecting  of  locations  in  terms  of  the  most  advantageously  locat- 
ed coal  deposits.  We  know  the  locational  figures  thus  created 
and  shall  consider  them  as  normal.  The  use  of  waterfalls  elimi- 
nates the  use  of  coal  deposits  and  involves  the  formation  of  new 



locational  figures  using  places  with  waterfalls.  But  this  means 
that  the  locations  in  the  new  figures  are  transferred  to  a  point 
which  may  be  theoretically  new,  namely,  to  the  waterfalls.  What 
is  theoretically  new  (as  compared  with  simply  eliminating  cer- 
tain deposits  of  coal  by  using  cheaper  or  otherwise  more  advan- 
89  tageous  deposits)  is  the  fact  that  a  fundamental  transfer  of  the 
location  in  the  figure  takes  place  on  account  of  the  necessity  of 
having  the  location  at  the  place  of  the  waterfalls.  Therefore  in 
all  cases  in  which  the  location  in  the  old  figures  was  not  at  the 
deposit  of  the  power  material,  fuel,  it  will  be  forced  to  go  to  the 
deposit  of  the  new  power  material,  the  waterfalls.  From  this  it 
follows,  formulating  our  conclusions  tentatively,  that  the  loca- 
tional effect  of  waterfalls  at  which  power  is  cheaper  and  better 
located  than  the  available  deposits  of  coal  will  not  be  as  great  as 
if  this  water  power  were  deposits  of  coal  offering  equal  advan- 
tage. For  the  effect  of  waterfalls  producing  water  power  is  les- 
sened by  additional  costs  of  transportation  which  result  when 
the  location  deviates  from  its  normal  point  of  minimum  trans- 
portation costs.  The  locational  revolution,  therefore,  which  will 
be  caused  by  water  power,  at  the  falls  will  be  less  than  if  this 
water  power  were  correspondingly  cheap  coal-power.  Its  influ- 
ence will  remain  less  to  the  extent  to  which  the  impossibility  of 
transporting  water  power  at  falls  necessitates  a  transfer  of  the 
location  within  the  figure.  This  transfer  will  be  most  extensive  in 
those  cases  in  which  the  former  location  was  least  influenced  by 
the  component  of  the  power  deposit. 

When  will  the  water  power  of  waterfalls  be  able  to  super- 
sede coal  deposits  and  to  draw  the  location  to  itself?  Evidently 
whenever  the  cost  of  power  saved  is  greater  than  the  cost  of  in- 
creased transportation.  We  shall  have  to  compare,  therefore,  the 
relation  between  the  cost  of  power  at  its  location  and  the  cost  of 
coal  at  its  deposit  with  the  relation  between  the  index  of  trans- 
portation costs  of  the  old  and  that  of  the  new  location.  If  the 
sum  of  the  cost  of  water  power  and  of  transportation  to  the 


water  power  location  is  smaller  than  the  sum  of  costs  of  coal  and 
of  transportation  to  the  coal  location,  then  the  water  power  is 
cheaper  and  supersedes  the  coal.  90 

To  give  an  example,  in  Figure  16,  P  is  the  old  location  with- 
in the  locational  figure  M^MoC  using  coal  (coal  at  M2);  W 
(waterfall)  is  the  new  location  in  the  locational  figure  M2WC 
using  water  power.  We  shall  have  to  compare  the  price  of  power 
per  unit  of  product  in  W  plus  the  index  of  the  transportation 
costs  of  W  {a'b')  with  the  price  (in  M2)  of  coal  used  per  unit  of 


product  plus  the  index  of  the  transportation  costs  of  P  (a,  b,  c). 
If  the  former  sum  is  smaller,  the  location  W  supersedes  P,  other- 
wise not.  This  shows  that  the  influence  of  non-transmittable 
water  power  is  rather  easy  to  calculate.  Its  influence  is  con- 
firmed within  the  narrow  limits  which  are  set  by  the  relation- 
ships of  cost  just  discussed.  Unless  the  distances  involved  are 
small,  the  influence  of  waterfalls  will  operate  most  directly  in  the 
case  of  industries  which  are  located  at  their  coal  deposits,  be- 
cause in  this  case  the  location  does  not  have  to  shift  within  the 

b)  Transmissible  water  power. — First,  we  shall  as  before 
substitute  theoretically  the  amount  of  coal  ordinarily  used  in 
producing  i  H.P.  for  the  electrical  H.P.  here  used.  The  price  of 
this  calculated  amount  of  coal  (at  the  water  power  location)  is 
to  be  compared  with  the  price  of  the  necessary  coal  at  the  coal 

^*As  it  had  to  in  the  above  example  where  the  location  had  to  go  from  a 
point  between  the  deposit  of  coal  and  the  deposit  of  the  other  material  to  the 
water  power  substituted  for  the  coal  deposit. — Editor. 


deposit.  Thus  we  have  expressed  theoretically  the  power  uti- 
lized in  terms  of  a  hypothetical  coal  deposit  which  would  have  a 
definite,  and  probably  on  the  whole,  a  lower,  price.  Second,  we 
shall  consider  the  cost  of  transmitting  the  H.P.  used  as  if  it  were 
the  cost  of  transporting  the  calculated  amount  of  coal.  On  the 
whole,  we  shall  find  that  locations  of  water  power  which  have 
good  electrical  transmission  yield  an  exceptionally  low  price  for 
the  power  as  calculated  in  terms  of  coal,  and  exceptionally  low 
91  rates  of  transportation  per  ton-mile.  The  effect  seems  clear  in 
this  case  of  transmissible  water-power,  for  it  theoretically  repre- 
sents deposits  of  especially  low-priced  coal  which  may  be  trans- 
ported at  exceptionally  low  rates.  The  very  low  price  of  such 
water  power  will,  in  accordance  with  our  previous  discussions, 
cause  its  use  to  a  larger  extent  than  its  geographical  location 
would  lead  one  to  anticipate,  and  will  eliminate  as  "locational 
comers"  the  use  of  coal  deposits  more  favorably  located  geo- 
graphically. The  low  ton-mile  rates  of  such  water  power,  as  cal- 
culated in  terms  of  coal,  may  be  expressed  in  theoretical  weight 
deductions  of  this  ''theoretical"  coal.  They  will  shift  the  loca- 
tion in  the  appropriate  locational  figures  toward  the  other  loca- 
tional  corners — the  places  of  consumption  and  the  other  mate- 
rial deposits — much  further  than  would  have  been  the  case  in 
the  locational  figures  formed  by  the  eliminated  coal  deposits. 
As  in  the  cases  when  non-transmissible  water  power  was  used, 
we  find :  ( i )  The  formation  of  new  locational  figures  results  from 
the  use  of  water  power;  and  (2)  a  transfer  of  the  location  takes : 
place  within  these  figures  according  to  theoretical  principles.. 
The  situation  differs  from  the  previous  case,  however,  because] 
the  location  is  not  shifting  toward  the  power  material  deposit^ 
but  rather  in  the  opposite  direction — that  is,  toward  the  placesi 
of  consumption  and  toward  the  other  material  deposits.  The! 
transfer  of  the  location  within  the  new  locational  figures  is,  how- 
ever, due  to  the  easy  transportation  of  the  new  power  materials,j 
and  not  to  their  immovability. 


From  these  observations  we  may  deduce  the  great  and  essen- 
tial difference  between  transmissible  and  non-transmissible  wa- 
,  ter  power.  While  in  the  case  of  non-transmissible  water  power 
the  transfer  of  the  location  from  the  point  of  minimum  costs  of 
transportation  raises  the  index  of  transportation  costs,  and  there- 
by narrows  the  ^'sphere  of  influence"  of  such  places  of  water 
power,  in  the  case  of  transmissible  water  power  the  low  cost  of 
transporting  the  equivalent  of  i  H.P.  gives  additional  momen- 
tum to  the  expansion  of  the  sphere  of  influence  already  extended 
by  the  low  cost  of  production.  For  it  is  quite  obvious  that  the  92 

low  rates  for  transporting  electrical  current  (low  ton-mile  rates 
of  the  ''theoretical"  coal)  mean  a  lower  index  of  transportation 
costs  of  the  respective  figures,  and  thereby  put  these  locational 
figures  on  a  basis  which  permits  them  to  compete  with  other 
locational  figures.  If  the  H.P.  can  be  produced  and  transmitted 
sufficiently  cheaply,  favorably  located  water  power  will  cause  a 
great  number  of  locational  figures  based  on  coal  to  be  eliminat- 
ed, and  just  as  many  locations  to  be  shifted.  On  the  other  hand, 
even  unfavorably  located  water  power  will  not  necessarily  be  ex- 
cluded from  becoming  the  basis  of  location  and  production. 

We  shall  be  able  to  determine,  according  to  our  theory,  ex- 
actly to  what  extent  and  with  what  locational  results  these  stores 
of  water  power  will  enter  into  modern  economic  life.  Using  the 
diagram  of  the  last  example,  the  location  P'  (based  upon  the 
water  power  in  W  instead  of  the  coal  deposit  M2)  will  not  be  lo- 
cated at  W  (as  in  the  case  of  non-transmissible  water  power), 
but  in  the  new  locational  figure  MJVC,  and  will  be  nearer  M^ 


and  C  than  the  former  location  P,  based  upon  coal  in  the  figure 
Mil/oC.  Its  position  within  the  new  figure  is  determined  by  the  _ 
laws  which  we  now  know  so  well  from  the  previous  discussions. 
The  weight  which  has  to  be  applied  on  the  component  WP'  ob-< 
viously  is  the  difference  between  the  weight  of  the  "theoretical" 
coal  (water  power  calculated  in  terms  of  coal)  which  is  brought 
from  W  and  the  weight  deduction  which  has  to  be  made  along 
this  line  corresponding  to  the  lower  rate  per  ton-mile.  In  order 
to  determine  whether  the  location  P'  is  possible  and  M.  should! 
be  eliminated,  we  shall  have  to  add  the  price  of  the  ''theoretical 
coal"  (water  power  in  terms  of  coal)  to  the  index  of  the  trans- 
portation costs  of  the  location  P\  This  sum  has  to  be  compared 
with  the  sum  of  the  index  of  transportation  costs  of  the  old  loca- 
tion P  and  the  price  of  actual  coal  per  unit  of  product  (at  M2) 

93  If  the  first  sum  is  smaller,  P'  is  possible;  otherwise  not.  This  ex- 
ample is  apparently  capable  of  general  application.  The  possi- 
bility, then,  of  fitting  water  power  and  its  effect  into  the  theory 
of  the  transportation  orientation  is  obvious.  We  may  well  sa>| 
that  we  have  succeeded  in  applying  our  theory  to  all  modifica 

94  tions  of  complete  modern  reality. 





I  The  labor  costs  of  an  industry  (in  the  sense  in  which  we  de- 
fined this  concept  in  the  preliminary  analysis  of  the  locational 
factors)  are,  in  general  economic  terms,  the  expenditures  of  hu- 
man labor  incurred  in  carrying  out  the  particular  process  of 
production.  They  appear  in  the  capitalistic  system  as  wages  and 
salaries  which  are  paid  out  in  the  course  of  the  productive  proc- 
ess, and  denote  the  "equivalent"  of  the  labor  used.  It  is  obvious, 
of  course,  that  human  labor  is  not  paid  for  with  "wages,"  be- 
cause it  is  something  different  from  a  "commodity."  However, 
the  economic  expression  of  the  energies  expended  in  labor  (that 
is,  the  "cost  of  labor"  of  which  we  are  now  speaking)  are  in  the 
capitalistic  economy  of  today  the  wages  and  salaries  which  are 
paid  out  per  unit  of  product.  And  since  we  always  deal  with 
economic  phenomena  in  their  concrete  present  form — for  only 
thus  do  they  become  comprehensible — we  shall  in  our  further 
discussion  deal  with  this  sort  of  wages  and  salaries,  calculated 
for  the  "unit  of  weight"  of  the  product  of  our  previous  theoreti- 
:al  discussion. 

These  labor  costs  can  only  become  factors  in  location  by 
/arying  from  place  to  place.  That  is  self-evident.  But  it  is  im- 
portant to  reaHze  that,  since  we  are  still  investigating  the  re- 
gional distribution  of  industry,  such  local  differences  of  labor 
:osts  concern  us  only  in  so  far  as  they  are  of  significance  for  this 
)roblem.  This  means  that  they  concern  us  only  if  in  some  man-  95 
ler  they  are  connected  in  fact  with  geographically  defined  points, 
»ecause  only  in  that  event  can  they  attract  industry  to  particu- 



lar  geographical  points  and  thus  have  an  effect  on  the  fundamen 
tal  regional  distribution  of  industry.  Only  a  part  of  the  actual 
local  differences  in  labor  costs  possesses  that  sort  of  peculiar  ge 
ographical  relationship.  The  labor  costs  of  an  industry  may 
differ,  speaking  generally,  on  account  of  two  quite  different  sets 
of  causes:  (i)  because  of  differing  levels  of  efficiency  and  of 
wages  of  labor,  i.e.,  for  more  or  less  subjective  reasons;  and  (2) 
because  of  differing  levels  of  efficiency  in  the  organization  and 
the  technical  equipment  with  which  the  laboring  force  is  set  to 
work,  i.e.,  for  more  or  less  objective  reasons.  However,  only  lo 
cal  differences  resulting  from  subjective  reasons  have  the  req 
uisite  peculiar  geographical  relationship — are  geographically 
''fixed."  They  are  fixed  differences  in  so  far  as  they  are  a  func- 
tion of  a  given  geographical  distribution  of  population,  which 
shows  different  levels  of  wages  and  of  performance  in  its  various 
parts.  On  the  other  hand,  the  differences  of  labor  costs  on  ac- 
count of  different  levels  of  efficiency  of  the  ''apparatus"  are,  i1 
seems,  no  more  geographically  determined  than  is  the  use  of  the 
apparatus  itself.  These  latter  differences  may  become  a  factpi 
determining  location  in  a  manner  that  is  to  be  taken  up  later  ir  1 
the  theory  of  agglomeration ;  but  at  the  present  moment  they  an 
outside  our  discussion. 

We  do  not,  therefore,  exhaust  at  present  the  significance  0 
labor  costs  as  a  locational  factor;  for  we  deal  only  with  that  par  | 
of  the  differences  of  labor  costs  which  results  from  local  differ! 
ences  in  the  level  of  personal  efficiency  and  wages  of  the  popuj 
lation.  I 

What  particular  circumstances  caused  these  differences  01 
wages  and  efficiency  and  the  consequent  differences  of  laboi; 
costs  is  a  matter  of  indifference  to  us  and  to  the  whole  "pure' 
theory.  Especially  does  it  not  concern  us  that  their  actual  leve 
is,  of  course,  not  a  phenomenon  of  "pure"  economics,  but  rathei 
a  changing  consequence  of  extremely  varied  historical  and  nat 
96  ural  circumstances.  All  this  may  be  neglected  by  pure  locationaj 


theory  which  is  only  concerned  with  investigating  the  funda- 
mental significance  of  such  geographically  determined  differ- 
ences of  labor  costs.  And  for  that  purpose  the  actual  level  of 
these  costs — and  even  whether  they  actually  exist — is  a  matter 
of  complete  indifference.  Pure  theory  conceives  them  as  a  ^'pos- 
sibility,"  and  investigates  the  theoretical  results  of  that  possi- 

In  one  thing,  however,  we  must  be  interested,  namely,  in  the 
geographically  essential  ''form"  in  which  these  differences  of 
cost  appear.  We  must  know  in  what  general  manner  the  labor 
costs,  as  determined  by  the  different  levels  of  wages  and  per- 
formance, are  actually  geographically  distributed  in  a  country 
at  a  given  moment.  Are  the  differences  ''according  to  area,"  so 
that  one  may  say  this  whole  region  operates  more  cheaply  than 
a  given  other  one?  Or  are  they  "according  to  place,"  so  that 
they  relate  to  particular  towns,  or  at  any  rate  to  more  or  less 
concentrated  districts  which,  in  a  general  way,  may  be  treated 
"as  a  town"  (a  mathematical  point)  without  committing  too 
great  an  error?  Whether  one  or  the  other  of  these  two  possi- 
biHties  is  assumed  will  be  of  considerable  significance  for  our 
discussion,  which  is  to  be  carried  on  by  means  of  mathematical 
aids.  In  the  first  case  we  shall  have  to  deal  with  the  mathemati- 
cal concept  of  the  "plane";  in  the  second,  with  that  of  the 

If  in  this  connection  we  are  to  approach  the  actual  situation 
without  prejudice,  we  must  make  various  distinctions  with  re- 
gard to  the  kinds  of  differences  in  wage  levels. 

We  will  at  once  recall  certain  differences  in  the  wage  level 
according  to  districts.  The  higher  general  level  of  wages  in  west- 
ern and  southern  Germany  as  compared  with  that  of  the  eastern 
Dart  may  occur  to  us  as  an  example.  We  may  think  of  the  fa- 
niliar  tables  of  average  local  day  wages  which  can  be  compiled 
from  the  sickness  insurance  data;  we  may  remember  that,  with 
:ertain  exceptions,  the  wage  scales  fall  "like  a  staircase"  from 


west  to  east;  and  that  pointlike  exceptions  to  this  regional  dis- 
tribution of  wage  levels  are  in  general  caused  only  by  the  large 
97  cities.  If  we  think  of  these  familiar  facts,  the  'Vage  rate"  will 
appear  to  us  as  a  result  of  a  superficial  examination,  as  essen- 
tially differentiated  ''according  to  area." 

And  yet  this  picture  is  one  of  many  statistical  simplifications 
which  we  are  always  using,  and  which,  though  not  actually; 
wrong,  gives  us  an  idea  of  reality  dangerously  inexact  in  detail. 

As  evidence  for  this  statement  let  us  cite  statistics  of  wagesi 
as  given  in  their  annual  report  for  190 1-2  by  one  of  the  largest 
German  unions  composed  mainly  of  unskilled  workers,  the  Cen- 
tral Union  of  Trade,  Transport,  and  Traffic  Laborers  (i.e.,  jan- 
itors, packers,  market  workers,  coachmen,  cab  drivers,  furniture« 
movers,  etc.).  The  figures  are  best  for  central  Germany  where 
the  Union  is  most  widely  extended  outside  the  large  cities.  The< 
average  weekly  wages  of  its  members  in  marks  show,  in  the  small! 
district  in  the  vicinity  of  the  Harz  Mountains,  the  following  va^ 
riations:   Nordhausen,  14.2;  Sangerhausen,  12.0;  Halberstadt 
15.7;  for  the  district  of  the  southern  Thuringian  Forest,  alsc- 
not  a  large  one — Sonneberg,  15.7;  Suhl,  15.3;  Saalfeld,  17.2; 
Erfurt,  19.3 ;  Jena,  17.0;  and  for  the  region  on  the  border  of  thu 
Saxon  industrial  area — Zeitz,  17.8;   Greiz,  16.7;   Plauenscheii 
Grund,  19.4.  Here  we  have  in  each  district  differences  of  from 
M.  2  to  M.  2.70  in  the  weekly  wage,  i.e.,  differences  of  up  to  2i 
per  cent  in  places  very  close  together.  Similar  results  are  sef 
ever5rwhere.  In  two  adjoining  Silesian  counties,  those  of  Stric 
gau  and  Waldenburg,   for  instance,  12.9  and  15.3  are  paid 
Hence  we  find,  even  for  unskilled  labor,  wage  rates  differing  en 
tirely  "according  to  place,"  not  only  in  the  large  towns  whercj 
wage  levels  are  naturally  well  above  those  in  the  surrounding 
country,  but  everywhere  else,  even  in  the  small  places  in  th4 
country  itself.  The  difference  "according  to  areas"  is  only  th(i 
general  average  of  very  large  local  differences. 

If  it  is  not  permissible  to  assume  a  regional  distribution  0: 



wage  level  even  for  that  meanest  category  of  labor  which  may 
most  truly  be  spoken  of  as  a  homogeneous  mass,  evidently  when 
we  study  the  wage  levels  of  skilled  labor  our  guiding  principle 
ought  to  be  that  wage  levels  will  be  distributed  ''according  to 
places."  According  to  the  report  of  the  Union  of  Metal  Workers  98 
for  1903,  pattern-makers  (in  sand),  for  instance,  earn  for  piece 
work  in  pfennig  per  hour  in  central  Germany:  in  Hildesheim, 
41;  Ilsenburg,  27;  Thale,  39;  Sangerhausen,  34;  Gotha,  44 — a 
range  of  1 7  pfennig,  or  60  per  cent,  in  the  small  districts  around 
the  Harz;  in  Zeitz,  24;  in  the  nearby  Gera,  34 — a  range  of  10, 
or  about  30  per  cent;  in  Bunzlau,  31 ;  Hirschberg,  42 ;  Schweid- 
nitz,  39 — a  range  of  11,  or  32  per  cent.  According  to  the  very 
complete  and  careful  reports  of  the  Wood-workers  Union  for 
1902,  skilled  wood-workers  (carpenters,  turners,  etc.)  earn  on 
the  average  per  week  in  mark:  in  Frankenhausen,  13.6;  Kalbe, 
1 1.2;  Sangerhausen,  16.7;  Schkeudnitz,  21;  Korbetha,  12; 
Naumburg,  18.7 — differences  of  9.8  marks  or  86  per  cent  per 
(Week  within  the  small  district  between  the  Goldene  Aue  and  El- 
ster-Saale. Similar  differences  appear  elsewhere.  The  Thurin- 
^ian  Forest  shows  the  following  figures:  Koburg,  14.7;  Weimar, 
21;  Gotha,  20;  Eisenach,  18.2 — in  other  words,  differences  of 
3.3  per  week. 

All  these  are  local  differences  in  the  small  towns  and  in  the 
'arming  country;  if  we  take  the  large  cities  into  consideration, 
he  local  differences  are  much  larger  still.  For  pattern-makers  it 
s  only  necessary,  for  instance,  to  extend  our  view  from  the  Harz 
0  Magdeburg  and  Hanover.  There  we  find  average  wages  per 
lOur  of  48-52  pfennig,  wages  approximately  twice  as  high  as 
hose  of  Ilsenburg  in  the  Harz.  Similarly  for  wood-workers, 
wcipzig  with  23.7  or  Halle  with  22.3  have  twice  the  wages  of 
Lorbetha  with  1 2  or  Kalbe  with  1 1 .2 . 

Therefore  the  wages  even  for  unskilled  labor,  but  much  more 
or  skilled  labor,  form  today  a  rather  mountainous  terrain  with 
eep  gorges  and  relatively  high  peaks.  So  far  as  wages  come  into 


consideration  we  shall,  even  when  differences  of  general  level 
form  a  broad  foundation  for  whole  regions,  think  of  variations 
from  point  to  point. 

Now  it  is  well  known  that  differences  of  wage  level  do  not 
give  an  adequate  idea  of  the  differences  in  the  level  of  labor  > 
costs.  The  parallelism  between  them  is  disturbed  by  differences 
99  of  efficiency.  There  are  two  possible  cases :  A  difference  in  effi- 
ciency conditioned  by  natural  and  cultural  facts  (nature  of  pop- 
ulation and  environment)  may  exist  at  the  same  wage.  This  is  a 
local  difference.  Also  the  results  of  the  fact,  well  known  empiri- 
cally to  social  psychology,  that  high  wages  and  high  efficiency  go 
together  may  disturb  things  to  a  considerable  extent.  The  latter 
theorem  would  mean  that  the  rather  mountainous  picture  of 
wage  differences  would  be  reflected  as  less  mountainous  differ- 
ences of  cost  of  labor.  It  might  even  mean  a  complete  smoothw» 
ing  out  of  hills  and  valleys;  or  it  might  even  go  beyond  that,  sc< 
that  places  with  high  wages  would  be  places  of  low  labor  costs 
In  the  empirical  theory  it  will  become  evident  that  for  indus-(| 
tries  of  a  particular  sort  that  may  in  fact  often  be  the  situa^< 
tion.  At  this  time  it  is  sufficient  to  point  out  that  whether  th 
differences  of  labor  cost  run  more  or  less  parallel  to  those  oi 
wages,  or  whether  on  account  of  differences  of  efficiency  the  t 
diverge  greatly,  as  a  matter  of  fact  today  every  employer 
every  industry  reckons  (as  a  result  of  his  experience)  with  thi: 
"local,"  and  not  with  the  ''regional,"  nature  of  the  differences  u 
the  cost  of  labor.  We  have  attempted  to  make  clear  the  locai 
variation  of  these  differences  by  citing  examples  of  the  extraordi 
narily  large  jumps  of  wage  rates  from  place  to  place,  and  thi:i 
explains  why,  in  the  pure  theory,  we  do  not  start  from  regionalj 
but  from  local,  variations  of  labor  costs.  We  shall  not  speak  o 
''areas  of  labor  cost"  on  different  levels,  but  of  labor  locations 
with  different  costs. 

As  has  been  indicated  in  the  general  introduction,  it  will  b 
necessary  for  the  present  to  disregard  a  number  of  qualitie 


which  these  labor  locations  in  fact  possess  in  order  to  make  the 
effect  of  their  varying  levels  of  costs  perfectly  clear  as  a  factor 
in  the  theory  of  location.  We  must  neglect  the  fact  that  an  un- 
limited supply  of  labor  is,  of  course,  not  to  be  had  at  any  of  these 
locations  at  a  given  time  at  the  cost  which  it  offers,  and  that 
therefore  it  cannot  attract  unhmited  numbers  of  industries  sim- 
ply by  virtue  of  this  cost  level.  We  must  also  leave  out  of  con- 
sideration the  fact  that  the  cost  level  of  each  location  is  altered 
by  every  movement  of  industry,  on  account  of  the  change  in  de- 
imand  for  labor  which  this  movement  causes.  We  must  disre-  loo 
,  gard  these  things  and  imagine  the  cost  levels  of  the  locations  to 
be  fixed,  and  the  labor  supply  available  at  each  location  to  be 
unlimited;  for  only  by  so  doing  can  we  analyze  clearly  and  to  its 
i  final  consequences  the  effect  which  the  differences  of  costs  will 
have  on  the  distribution  of  industry.  Only  if  we  conceive  the  at- 
tracting power  of  each  location — which  power  is  based  upon 
these  differences  of  cost — as  freed  from  all  limits  but  those  of 
space,  that  is  to  say,  only  if  we  conceive  it  as  actually  unlimited, 
can  we  clearly  trace  its  effect  upon  location.  And  it  is  necessary, 
of  course,  to  introduce  this  attracting  power  as  a  fixed  quantity; 
otherwise  it  could  not  be  measured  in  mathematical  terms. 
Hence  we  must  regard  the  differences  of  cost  as  ''given";  and  as 
given  with  unlimited  attracting  power. 

We  shall  leave  it  to  empirical  theory  to  eliminate  these  as- 
sumptions and  to  introduce  into  the  picture  the  actual  environ- 
ment within  which  these  abstract  laws  work  out,  the  significant 
elements  of  the  actual  environment  being  variability  of  the  dif- 
ferences, and  the  connection  of  these  differences  with  the  com- 
petition among  industries  for  what  is  at  any  given  time  only  a 
'imited  supply  of  labor  at  each  location.  Only  through  recourse 
;o  such  empirical  analysis  can  the  local  movements  of  labor  and 
he  general  changeability  of  the  ground  work  of  industrial  labor 
:ost  be  taken  account  of  and  explained. 



How  does  this  groundwork  of  labor  cost  effect  the  orienta- 
tion of  industry  by  means  of  its  locations  of  different  labor  cost 
levels?  J 


Let  us  imagine  again  an  isolated  process  of  production  and 
distribution  with  its  raw  material  deposits  and  its  place  of  con- 
sumption. The  point  of  minimum  transportation  costs  results 
from  this  locational  figure  and  from  the  composition  of  the 
well-known  material  index.  What  significance  will  it  have  for  de- 
termining whether  production  will  really  take  place  at  this  point 
that  in  the  infinite  area  surrounding  it  there  are  perhaps  points 
at  which  a  ton  of  product  can  be  produced  with  smaller  labor 
1 01  costs? 

The  following  is  at  any  rate  clear:  that  every  such  point  of» 
lower  labor  costs  constitutes  economically  a  center  of  attractioi 
which  tends  to  draw  industry  away  from  the  point  of  minima 
transportation  cost  to  itself.  But  the  attraction  of  such  a  cent« 
is  essentially  not  an  attraction  of  a  mere  approach;  for  an  ap 
proach  to  the  location  with  the  lower  labor  costs  would  have  n( 
advantage  for  the  industry.  Only  a  migrating  to  that  place  itself 
would  be  of  use  to  it;  hence  there  is  here  the  issue  of  an  alterna- 
tive attraction:  the  question  is  whether  industry  should  operat 
at  the  point  of  minimum  transportation  costs  or  be  moved  to  the 
labor  location. 

Under  what  circumstances  will  industry  be  moved  to  the  la- 
bor location,  and  when  will  it  not? 

Every  change  of  location  away  from  the  point  of  minimum^ 

^  Isodapane  is  a  new  technical  term  introduced  by  Alfred  Weber.  It  is , 
constructed  in  analogy  to  the  geographical  term  "isotherm."  Similar  words  are^ 
current  in  scientific  literature.  Isodapane  contains  besides  the  well-known  root 
isos,  "equal,"  the  word  dapane,  which  means  "expense,"  "cost." — Editor. 


transportation  costs  to  a  favorable  labor  location  means,  in  terms 
of  transportation,  a  ''deviation"  which  lengthens  the  transpor- 
tation routes  and  raises  transportation  costs  above  those  pre- 
vailing under  the  most  advantageous  conditions.  The  changes  of 
location  can  therefore  take  place  only  if  the  rise  of  cost  per  ton 
of  product  which  it  causes  is  compensated,  or  more  than  com- 
pensated, by  savings  of  labor  costs.  A  location  can  be  moved 
from  the  point  of  minimum  transportation  costs"  to  a  more  fa- 
vorable labor  location  only  if  the  savings  in  the  cost  of  labor 
which  this  new  place  makes  possible  are  larger  than  the  addition- 
al costs  of  transportation  which  it  involves.  It  is  necessary  to  un- 
derstand this  general  theorem  precisely,  and  to  analyze  its  con- 

To  understand  precisely  its  theoretical  significance  we  must 
bring  it  into  organic  connection  with  the  general  mathematical 
concepts  which  we  have  hitherto  used.  The  means  necessary  for 
this  task  are  provided  by  what  is  said  in  the  second  part  of  the 
appendix  about  curves  of  equal  transportation  cost.  The  discus- 
sion there  starts  from  the  assumption  that  any  deviation  from 
the  transportational  minimum  point  may  take  place  in  quite  dif- 
ferent directions ;  and  that  in  any  direction  in  which  it  may  go 
there  will  be  points  at  which  the  costs  incurred  in  such  deviation 
(i.e.,  the  additional  costs  of  transportation  per  ton  of  product 
caused  by  the  deviation)  are  equally  high.  From  this  it  follows  102 
that  there  must  also  be  curves  connecting  such  points  of  equal 
deviation  costs  which  may  be  drawn  around  the  minimum  point 
at  some  distance,  varying  in  accordance  with  the  index  of  ma- 
j  terials.  These  curves,  curves  of  equally  high  additional  cost  of 
'  transportation,  form  the  conceptual  connecting  link  between  the 
transportational  minimum  points  and  the  deviation  points  which 
represent  the  labor  locations.  We  shall  call  them  isodapanes  (of 
equal  cost),  for  brevity's  sake. 

^  This  point  is  hereafter  often  referred  to  simply  as  minimum  point. — Editor. 


For  every  labor  location,  wherever  situated,  there  must  be 
an  isodapane  of  the  respective  locational  figure.  This  isodapane 
indicates  how  high  the  costs  of  deviating  the  industry  from  the 
minimum  point  of  the  locational  figure  to  the  labor  location  in 
question  would  be. 

On  the  other  hand,  some  isodapane  of  the  locational  figure  in 
location  will  correspond  to  the  index  of  economies  of  the  labor 
question  in  such  a  way  that  the  deviation  costs  which  it  indicates 
per  ton  of  product  are  exactly  as  large  as  the  saving  in  labor 
costs  per  ton  of  product  as  compared  with  the  labor  costs  at  the 
minimum  point.  Hence  it  is  apparent  that,  if  the  labor  location 
lies  on  a  lower  isodapane  than  that  just  discussed,  its  economies 
exceed  the  deviation  costs;  if  it  lies  on  a  higher  one,  the  devia- 
tion costs  exceed  its  economies.  That  means  that  a  labor  location 
will  attract  the  industry  if  it  lies  within  the  area  of  this  isoda- 
pane, because  in  that  event  its  economies  are  greater  than  the 
deviation  costs  and  the  migration  to  it  will  cause  greater  econ- 
omy than  it  causes  increased  cost;  and  vice  versa,  it  ca7inot 
attract,  cannot  bring  about  the  migration  of  the  industry  if  it 
lies  outside  of  the  limits  of  this  isodapane,  for  in  that  case  the 
economy  is  smaller  than  the  deviation  costs.  With  regard  to  the 
attracting  power  of  this  labor  location,  this  is  the  critical  isoda- 
pane. To  every  labor  location,  no  matter  where  situated  with 
any  index  of  economy  whatever,  there  must  correspond  such  a 
103  critical  isodapane.  The  relation  of  the  labor  location  to  this 
critical  isodapane — whether  it  lies  inside  or  outside  of  it — de- 
termines whether  or  not  such  a  location  will  attract  the  produc- 
tion of  the  locational  figure  concerned. 

The  foregoing  analysis  has  brought  the  attracting  power  of' 
labor  location  (its  ability  to  substitute  "labor  orientation"  for 
"transport  orientation")  into  the  realm  of  precisely  determin- 
able laws,  the  conditions  of  which  have  for  the  individual  case 
been  sufficiently  clarified  by  the  foregoing. 




It  remains  to  introduce  into  the  framework  of  our  general 
discussion  the  conditions  under  which,  in  the  individual  instance, 
deviation  and  labor  orientation  can  and  will  occur,  and  thus  to 
pass  on  to  the  general  conditions  on  which  labor  orientation  de- 
pends. In  this  connection  we  shall  ask  at  once  two  questions: 
First,  which  of  these  conditions  presents  characteristics  of  in- 
dividual industries;  and  second,  which  are  conditions  applying 
uniformly  to  all  industries — in  other  words  are  "environmental 
conditions"?  We  shall  see  that,  in  contrast  to  the  basic  trans- 
port orientation  of  industry,  which  through  the  material  index 
and  the  '^locational  weight"  depends  solely  upon  "character- 
istics" of  the  individual  industries,  the  amount  and  kind  of 
labor  orientation  is  essentially  determined  by  "environmental 

Let  us  first  deduce  the  various  possible  kinds  of  conditions 
from  the  individual  analysis  we  have  undertaken.  The  fol- 
lowing are  the  factors  on  which  the  deviation  of  an  industrial 
production  because  of  labor  locations  depends:  First,  the  geo- 
graphical position  of  the  location  figures  and  labor  locations. 
Second,  the  course  of  the  isodapanes  around  the  minimum  points 
of  the  locational  figures.  Third,  the  indices  of  economy  of  the  104 
labor  locations  per  unit  weight  of  product. 

The  geographical  position  of  locational  figures  and  labor  lo- 
cations evidently  has  nothing  to  do  directly  with  the  general  char- 
acter of  the  various  industries.  It  is  a  seemingly  "accidental" 
fact  in  the  situation,  independent  of  the  character  of  an  industry. 
We  shall,  however,  later  put  this  fact  into  its  general  context 
and  take  it  out  of  the  sphere  of  the  individual  and  accidental  in 
which  it  seems  to  stand. 

The  course  of  the  isodapanes  around  the  minimum  points  of 
the  locational  figures  depends  upon  two  subordinate  factors. 
One  is  entirely  imphcit  in  the  nature  of  the  given  industry, 
namely,  its  material  index  and  the  locational  weight  dependent 



on  it.  The  figures  of  the  Appendix  show  (what  we  shall  presently 
discuss  more  in  detail)  how  completely  the  distance,  and  to 
what  degree  the  form  of  the  isodapane  is  dominated  by  this 
factor.  For  the  distance  of  the  isodapanes  from  each  other,  how- 
ever, a  second  factor  becomes  operative,  namely,  the  rates  of 
transportation  prevailing  at  any  given  time  in  a  region.  It  is 
clear  that  if  one  draws  around  a  point  lines  indicating  equal 
additional  transportation  costs,  i.e.,  lines  whose  distance  from 
each  other  is  determined  by  a  given  unit  of  additional  cost,  the 
actual  geographical  distance  of  these  lines  from  each  other  will 
be  determined  among  other  things  by  whatever  geographical  dis- 
tance the  unit  rate  of  costs  covers,  i.e.,  by  the  height  of  the  pre- 
vailing rates  of  transportation.  Here  we  have  a  further  condition 
of  labor  orientation  independent  of  the  character  of  individual 
industries  and  applying  equally  to  all  of  them. 

3.  In  order  to  see  upon  what  the  indices  of  economy  of  the 
labor  locations  per  unit  weight  of  product  depend,  we  shall  have 
to  inquire  how  such  an  economy  (for  example,  of  ten  marks  per 
ton  of  product)  works  out.  Evidently,  because  the  labor  costs 
per  ton  are  "compressed"  by  a  given  percentage,  5,  10,  20  per 
cent,  etc.,  the  index  of  economy  depends  first  upon  this  per- 
centage of  ''compression."  But  that  is  only  one  factor.  How 
great  the  total  absolute  economy  per  ton  will  be  depends  also,  it 
is  obvious,  upon  the  absolute  level  of  labor  costs  which  are  com- 
105  pressed.  If  these  costs  amount  to  M.  1,000  per  ton,  a  compres- 
sion of  10  per  cent  will  cause  an  index  of  economy  for  this 
labor  location  of  M.ioo  per  ton;  but  if  they  amount  to  only,  the  index  will  be  M.i.  This  absolute  amount  of  labor 
costs  per  ton  of  product  on  which  the  compression  is  based  (and 
which  is  in  a  certain  sense  the  object  of  this  compression)  evi- 
dently pertains  to  every  given  industry  of  a  country  in  a  given 
stage  of  development  in  the  form  of  average  costs  of  labor  which 
must  be  applied  to  the  ton  of  product.  We  shall  call  this  the  in- 
dex of  labor  cost  of  the  industry.  As  a  condition  of  labor  orienta- 



tion  the  labor  costs  accruing  per  ton  of  product  therefore  belong 
to  the  characteristics  of  the  particular  industries. 

The  percentage,  however,  by  which  a  given  labor  location 
compresses  this  index  of  the  cost  of  labor  of  an  industry  is  not  a 
peculiarity  of  the  given  industry  but  one  of  the  particular  labor 
location.^  Therefore  the  actual  percentage  of  compression  of  the 
labor  cost  indices  at  the  various  labor  locations  constitutes  a 
third  general  environmental  condition. 

There  are  thus  two  general  characteristics  of  industries  de- 
termining their  labor  orientation:  (i)  their  locational  weight 
(especially  their  index  of  materials),  and  (2)  the  index  of  their 
labor  costs.  And  there  are  three  environmental  conditions  deter- 
mining labor  orientation :  ( i )  the  geographical  position  of  loca- 
tional figures  and  labor  locations,  (2 )  the  rates  of  transportation, 
(3)  the  actual  percentages  of  compression  of  the  labor  cost 


Let  us  take  up  first  the  characteristics  which  we  have  said 
to  be  factors  in  determining  the  labor  locations  of  individual  in- 
dustries, that  is,  let  us  examine  the  manner  in  which  the  loca- 
tional weight,  or  index  of  materials,  and  the  index  of  labor  costs 
determine  labor  orientation.  106 


I.  Index  of  labor  costs. — The  significance  of  the  index  of 
labor  costs  is  very  simple  and  really  already  evident.  The  for- 
mula, according  to  the  foregoing,  will  run:  With  a  high  index  of 
labor  costs,  a  large  quantity  of  labor  costs  will  be  available  for 
compression,  with  correspondingly  large  potential  indices  of 
economy  of  the  labor  locations,  and  correspondingly  high  crit- 
ical isodapanes;  therefore  we  shall  find  a  high  potential  attract- 
ing power  of  the  labor  locations.  And  vice  versa:  low  index 
of  labor  costs,  small  quantity  of  labor  cost  available  for  com- 

^  This  is  certainly  true  for  the  labor  locations  of  the  same  industry. 


pression,  etc.  That  is  to  say,  the  potential  attracting  power  of 
the  labor  locations  runs,  for  the  different  individual  industries, 
parallel  to  the  indices  of  labor  costs  of  the  industries.  The  index 
of  labor  costs  is  the  provisional  standard  of  measuring  the  extent 
to  which  the  industries  may  be  deviated.  For  many  industries  it 
alone  decides  definitely  how  they  will  be  oriented ;  this  is  true  for 
all  those  in  which  the  labor  costs  are  so  low  that  they  are  insuf- 
ficient to  cause  effective  indices  of  economy.  The  other  indus- 
tries are  grouped  by  this  index  according  to  the  amount  of  labor 
they  require  per  ton  of  product,  which  primarily  indicates  to 
what  extent  they  may  be  deviated. 

2 .  The  locational  weight. — In  order,  however,  to  obtain  the 
actual  standard  for  measuring  to  what  extent  an  industry  may 
be  deviated,  we  must  take  into  consideration  the  locational 
weight  and  the  index  of  materials.  ) 

The  locational  weight  influences  the  extent  to  which  an  in- 
dustry may  be  deviated  through  its  effect  upon  the  distance  and 
form  of  the  isodapanes.  Speaking  first  of  the  distance  of  thel 
isodapanes,  the  manner  in  which  the  locational  weight  affects 
them  is  theoretically  very  simple:  low  locational  weight,  small! 
mass  of  material  per  ton  of  product  to  be  transported,  great  dis 
tance  of  the  isodapanes  from  each  other,  wide  extension  of  the 
critical  isodapane;  consequently  the  industry  may  be  deviat 
to  a  large  extent.  And  vice  versa.  The  locational  weight  repr 
sents  a  standard  which  further  determines  the  distance  of  th 
isodapanes  for  the  particular  industry.  To  the  extent  that  it  af 
fects  this  distance,  it  simply  provides  a  more  precise  determina 
tion  of  the  provisional  standard  furnished  by  the  index  of  laboi! 
107  costs  in  the  foregoing  formula. 

However,  the  locational  weight  affects  not  only  the  distance 
between  the  isodapanes  from  each  other  but  also  their  formsi 
It  does  so  through  the  size  and  composition  of  the  material  inde?l 
on  which  it  rests,  as  the  figures  of  the  Appendix  show.  It  can  also 
tell  us  that  the  tendency  of  a  given  industry  to  deviate  from  tht< 


minimum  point  is  not  necessarily  of  equal  force  in  all  different 
directions.  So  far  as  we  can  set  up  a  general  rule,  only  industries 
which  have  components  of  equal  strength  determining  their  lo- 
cation (and  hence  having  a  centrally  situated  location)  have  a 
tolerably  equal  tendency  to  deviate  their  location  from  the  mini- 
mum point  in  all  directions  (approximately  circular  form  of 
the  isodapanes).  An  industry  having  components  of  varying 
strength,  and  hence  an  eccentric  minimum  point  (i.e.,  with  a 
minimum  point  near  one  corner  or  in  it),  will  more  easily  deviate 
in  the  direction  of  the  strongest  corners  of  the  location,  and  the 
stronger  its  components  are,  the  more  it  will  do  so.  Expressed 
in  terms  of  the  use  of  materials,  the  industries  having  a  very 
small  material  index  (very  little  localized  material  and  hence 
preponderance  of  the  consumption-components)  and  industries 
having  a  very  high  material  index  (a  great  deal  of  localized  ma- 
terial and  hence  preponderance  of  some  material  component) 
will  deviate  unevenly  (deviation  in  the  direction  of  the  enlarged 
corners  being  easier).  Industries,  on  the  other  hand,  with  a 
medium  index  of  materials  (for  instance  of  the  size  of  2),  par- 
ticularly if  it  is  also  evenly  composed  (1:1),  will  deviate  more 
Dr  less  evenly  in  all  directions. 

All  this,  however,  is  not  of  very  great  importance.  It  is  of 

significance  only  for  deviations  over  short  distances,  really  only 

■or  deviations  which  lie  within  or  in  the  immediate  vicinity  of 

he  locational  figures.  For  all  greater  distances  the  isodapanes 

ipproximate  (as  the  figures  of  the  Appendix  show)  the  form  of 

■I  circle,  whatever  the  size  and  composition  of  the  material  index. 

\nd  this  is  quite  to  be  expected,  for  the  situation  of  the  location 

esulting  from  the  material  index  becomes  a  matter  of  indiffer- 

nce  for  great  distances,  for  which  the  locational  figure  approxi- 

lates  more  and  more  a  "point."  The  deviation  represents  more 

nd  more  transportation  back  and  forth  on  the  same  line,  and 

pll  therefore  be  equally  expensive  in  all  directions.  The  ma-  108 

^rial  index  of  an  industry,  through  the  form  which  it  gives  to 


the  isodapanes,  besides  its  effect  upon  the  distance,  becomes 
geographically  significant  for  small  deviations  by  altering  the 
^'direction"  in  which  such  deviation  would  turn  under  the  in- 
fluence of  the  index  of  labor  costs;  by  thus  altering  the  "direc- 
tion" of  possible  deviations,  the  material  index  affects  the  shape 
of  the  isodapanes,  besides  determining  their  distance  from  each 
other.  But  this  influence  disappears  for  greater  distances.  And 
since  the  geographical  difference  of  direction  is,  as  the  figures 
show,  none  too  great  even  for  the  short  distances  (for  the  isoda- 
panes even  then  approximate  rather  closely  the  form  of  circles), 
it  is  permissible  for  the  broad  purposes  of  our  theory  to  ignore 
the  material  index  in  so  far  as  its  significance  is  based  only  upon« 
the  non-circular  form  of  the  isodapanes.  The  theory  should  be^ 
allowed  to  proceed  as  if  all  isodapanes  were  circular;  in  which 
case  only  the  distance  resulting  from  the  absolute  quantity  of 
material  used  remains  for  determining  more  precisely  the  real 
deviating  significance  of  the  index  of  labor  costs  of  the  labor 
locations  through  the  locational  weight. 

3.  Locational  weight  and  coefficient  of  labor. — To  deter- 
mine more  precisely  through  the  locational  weight  the  real  devi- 
ating significance  of  the  index  of  labor  costs  measured  (it  will 
be  remembered)  by  the  number  of  tons  of  product,  we  have  to 
bear  in  mind  that  every  increase  of  the  locational  weight  dimin- 
ishes (by  contracting  the  isodapanes)  this  real  significance,  whil 
every  decrease  of  the  locational  weight  increases  the  significance 
The  real  deviating  significance  cannot  be  measured  by  weigh 
of  product  (as  has  been  done  by  the  index  of  labor  costs  so  far) 
but  only  by  locational  weight  (weight  of  product  plus  weight  oi|| 
localized  materials).  Expressed  differently,  the  amount  of  laboK 
costs  connected  with  the  locational  weight  of  a  given  industry 
in  the  coefficient  of  labor,  as  we  shall  call  it,  constitutes  the  gen 
eral  characteristic  determining  labor  deviation  of  the  industry.  |j 

Indeed,  it  is  quite  clear  that  if  the  form  of  the  isodapanes 
(i.e.,  the  different  degree  of  deviation  in  different  directions) 


may  be  disregarded,  it  is  the  locational  weight  that  has  to  be 
moved  if  a  deviation  is  to  take  place.  This  locational  weight, 
therefore,  is  the  only  factor  which  balances  the  actual  deviating 
influence  of  the  labor  costs  as  they  are  being  compressed.  But  if  109 
the  varying  degree  of  deviation  of  industry  in  various  directions, 
and  if  the  qualitative  determination  of  its  deviations  by  the  loca- 
tional weight  and  its  composition  are  matters  of  indifference, 
then  the  locational  weight  may  be  contrasted  with  the  amount  of 
labor  costs  simply  as  a  quantitative  measure  of  the  extent  of  its 
deviating  ability,  and  thus  be  made  the  basis  of  calculating  this 

The  concept  of  the  "labor  coefficient"  does  this.  It  might  be 
well  to  point  out  in  this  connection  that  these  labor  coefficients 
will  be  fractions,  like  100/3  (i-^-?  M.ioo  labor  cost  per  ton  of 
product  to  three  tons  locational  weight).  It  will  be  useful,  how- 
ever, to  get  the  labor  coefficient  of  different  industries  on  a 
fully  comparable  basis.  We  shall  therefore  reduce  it  so  that  the 
locational  weight  becomes  one.  In  other  words,  we  shall  ask 
how  much  labor  cost  will  arise  in  each  industry  for  one  ton  of 
locational  weight  to  be  moved.  We  shall  always  speak  of  the 
labor  coefficient  of  an  industry  in  the  sense  of  its  labor  costs  per 
ton  of  weight  to  be  moved,  per  locational  ton,  as  we  may  call  it.^ 

Using  the  term  labor  coefficient  in  this  sense,  we  shall  hence- 
forth say  that  the  labor  orientation  of  industries,  so  far  as  it  de- 
pends on  their  general  characteristics,  is  determined  by  their 
labor  coefficient. 

To  illustrate  the  significance  of  this  theorem  we  shall  give  a 
few  examples.  The  manufacture  of  corsets  has  a  labor  coefficient 
3f  about  M.I, 5 00;  the  pottery  industry,  of  about  M.55;  the 
Droduction  of  raw  sugar  (from  beets),  of  M.1.30.  According  to 
:hese  coefficients,  10  per  cent  of  labor  cost  saved  at  any  place 
iiieans  respectively  M.150,  M.5.50,  and  M.0.13  saved  per  loca- 

*  Every  such  locational  ton  must  be  thought  of  as  composed  of  amounts  of 
product  and  materials  corresponding  to  the  composition  of  the  locational  weight. 



tional  ton.  If  we  assume  a  ton-kilometer  rate  of  5  pfennig,  we 
find  that  the  corset  manufacture  might  deviate  3,000  km.,  the 
no  pottery  industry,  no  km.,  and  raw  sugar  production,  2.6  km. 
The  entire — and  immensely  different — manner  of  orientation  of 
these  three  industries  is  explained  by  these  figures. 


We  have  spoken  hitherto  of  the  location  of  isolated  individ- 
ual productive  units  which  are  being  deviated.  It  is  not  difficult 
to  visualize  the  evolution  of  the  orientation  of  an  entire  industry 
under  the  influence  of  the  labor  coefficient  and  of  its  compressi- 
bility. It  is  quite  easy  to  get  a  picture  of  this  orientation.  We 
should,  first,  consider  how  far  the  individual  productive  units  of 
a  given  industry  may  deviate  from  the  minimum  points  of  the 
individual  locational  figures,  this  being  determined  by  the  par- 1 
ticular  labor  coefficient.  And  we  should,  second,  remember  that( 
theoretically  each  attracting  labor  location  will  influence  all  the 
locational  figures  of  an  industry,  wherever  they  may  be  situated 
and  that  each  attracting  labor  location  has  a  tendency  to  attract 
production  from  all  sides  to  itself.  From  these  two  considera- 
tions we  get  the  picture  of  production  piling  up  at  the  labor  loca- 
tions, coming  from  various  directions.  It  is  important  to  observe 
that  the  number  of  locations  where  they  will  pile  up  is  related  to 
the  extent  of  the  deviation.  This  last  shading  of  the  picture  may 
also  be  seen  by  combining  the  two  considerations.  For  if  the 
attraction  of  the  labor  locations  of  an  industry,  affecting  as  i1 
does  the  locational  figures  from  all  sides,  is  effective  over  large 
areas,  this  will  mean  an  effective  competition  of  the  variom 
labor  locations  with  each  other.  Some  labor  locations  of  the 
same  industry  will  compress  the  labor  costs  more,  and  therefore' 
some  will  exert  a  stronger  attraction  than  others.  Those  whidl. 
attract  more  strongly — which  attract  with  the  larger  percent!, 
age  of  compression — will  eliminate  those  which  attract  lesJl 
strongly.  Within  the  radius  in  which  they  are  effective  (depend  i 


ing  on  the  character  of  the  industry)  they  will  draw  production 
to  themselves  from  all  sides.  This  power  of  attracting  industries 
from  all  sides,  of  eliminating  the  "weak,"  will  be  proportionate 
to  the  effect  of  the  labor  locations  of  a  given  industry,  and  this 
effect  depends  upon  the  extent  to  which  an  industry  will  deviate. 
The  result  will  be  that  industries  deviating  to  a  high  degree  will 
agglomerate  in  a  small  number  of  labor  locations,  while  indus- 
tries with  a  low  degree  of  deviation  will  remain  distributed  over 
many  locations.  1 1 1 

As  a  result  of  our  consideration  of  the  labor  coefficient  we 
can  state  the  following  rule  about  the  orientation  of  an  entire  in- 
dustry: Since  the  deviation  of  an  industry  depends  on  the  size  of 
its  labor  coefficient,  the  industry  will  be  concentrated  at  a  smaller 
number  of  labor  locations,  will  tend  to  be  more  strongly  oriented 
according  to  labor,  the  higher  its  labor  coefficient  is. 

All  this  is  clear,  and  would  have  been  accepted  as  true  even 

before  the  idea  of  orientation  as  a  whole  had  been  set  forth  in 

detail  as  we  have  just  done.  We  could  now  leave  the  subject  of 

the  orientation  of  an  entire  industry  if  there  were  not  still  one 

point  relating  to  the  "concentration"  which  should  be  clarified. 

This  point  concerns  an  alteration  in  the  attracting  power  of  the 

labor  locations  which  takes  place  through  (hindurchgeht)  an 

alteration  in  the  costs  of  transportation  in  the  process  of  con- 

'centration.   Let  us,  for  example,  imagine  the  simplest  case  in 

which  the  production  of  two  locational  figures  is  concentrated 

at  one  labor  location,  as  is  shown  graphically  in  the  Figure  18 

shown  on  p.  115.  The  labor  location  to  which  the  industry  is 

attracted  would  draw  each  of  the  raw  materials  which  it  needs 

'from  a  different  material  deposit  (the  first  materials  from  Mx 

nd  M\,  and  the  second  from  M2  and  M'2,  and  if  the  industries 

f  more  than  two  locational  figures  were  attracted,  it  would  draw 

from  as  many  material  deposits  as  there  were  locational  figures 

Dresent,  assuming  that  the  industry  of  each  of  the  locational 

igures  had  its  own  material  deposits.  It  is  clear,  however,  that 


for  each  of  the  materials  used  there  is  one  deposit  which  is  most 
favorably  situated  in  relation  to  the  labor  location.  And  it  is 
quite  evident  that,  assuming  a  sufficient  productivity  of  this 
most  favorably  situated  deposit,  the  industry  when  removed  to 
the  labor  location  will  no  longer  need  the  less  favorably  situated 
materials  which  it  made  use  of  in  the  individual  figures.  It  will 
therefore  "close  down"  those  deposits  and  cover  its  needs  from 
112  the  one  most  favorably  situated.  In  our  case  this  will  mean  that 
Ml  and  M\  will  be  closed  down,  and  the  whole  demand  for  raw 
materials  will  be  supplied  from  M2  and  M\.  A  labor  location 
which  has  attracted  plants  will  be  connected  with  all  the  in- 
dividual locational  figures  of  the  industry  only  through  the  mar- 
kets for  which  it  produces,  and  not  any  more  through  their  ma- 
terial deposits;  and  it  markets  its  goods  "all  over  the  world"  (as 
we  can  daily  observe),  while  it  uses  only  the  nearest  deposits  oj 
sufficient  productiveness  for  its  raw  material. 

The  closing  down  of  raw  material  deposits  which  is  the  char- 
acteristic feature  of  this  phenomenon  takes  place  for  the  pur 
pose  of  saving  unnecessary  costs  of  transportation.  Its  result  i: 
that  in  every  locational  figure  whose  industry  is  diverted  th«< 
total  deviation  costs  of  the  old  locational  figure  are  no  longer  s( 
up  against  the  labor  economy  which  the  diverting  labor  locatioi 
offers ;  from  these  deviation  costs  the  amount  of  transportatioi 
costs  saved  by  using  the  most  favorable  deposits  is  now  to 
subtracted.  In  our  case  the  economy  which  A  offers  is  no  longe^ 
contrasted  to  the  full  deviation  costs  of  Mi  Mo  C  or  M'l  M\  C:\ 
since  so  far  as  the  deviation  of  the  first  triangle  is  concernec 
these  deviation  costs  are  to  be  lessened  by  the  transportatioi 
costs  saved  by  substituting  M'l  for  Mi ;  and  so  far  as  the  devn 
tion  of  the  second  triangle  is  concerned,  by  the  economy  whicli 
the  substitution  of  M2  for  M'2  offers.  These  economies  of  transj 
portation  are  evident  from  the  different  length  of  the  hues  to  th' 
deposits.  Cf.  Fig.  18  on  next  page. 

Now  in  order  to  make  this  tendency  even  clearer  we  ma; 


express  the  matter  the  other  way  around.  We  may  say:  to  the 
economy  which  the  labor  location  offers  through  lower  costs  of 
labor  is  added  that  which  it  gains  through  replacement  of  the 
material  deposits.  Therefore  in  order  to  make  clear  the  actual 
attracting  power  of  a  labor  location  in  relation  to  any  given  loca- 
tional  figure  we  shall  have  to  set  against  the  deviation  costs  of 
this  locational  figure,  not  simply  the  index  of  labor  economy  of 
ithe  location,  but  also  the  economies  gained  through  the  replace- 
ment of  material  deposits.  Only  in  this  manner  shall  we  gain  a 


Mi  Ml 

Fig.  19 

measuring  rod  for  the  attracting  power  of  the  labor  location, 
irst,  in  its  effect  upon  each  individual  locational  figure,  and  sec- 
ond, in  its  compound  effect  upon  all  locational  figures  which  fall 
vithin  its  circle  of  influence.  And  only  thus  do  we  gain  a  correct  113 
heoretical  picture  of  the  orientation  of  an  industry  as  a  whole, 
md  of  the  magnitude  and  form  of  its  concentration  at  the  labor 

It  may  even  be  that  new  deposits  of  materials  are  called  into 
)lay  by  such  a  deviation.  This  opening  up  of  new  deposits,  as 
Veil  as  the  replacement  of  material  deposits,  may  have  essential 
ignificance  with  respect  to  the  competition  of  the  labor  loca- 
:  jions  with  each  other,  and  may  codetermine  the  deviation  of 
■  tidustry.  It  is  obvious  that  new  deposits  may  be  brought  to  light 
^y  the  deviation.  For  the  utilization  of  material  deposits  natu- 
ally  need  not  be  limited  to  those  originally  connected  with  the 
Dcational  figures,  but  may  obviously  include  deposits  hitherto 


not  used,  which  lie  in  the  vicinity  of  the  labor  location.  Figure 
19  shows  a  very  simple  case.  The  larger  or  smaller  chances  of 
making  use  of  favorably  situated  new  deposits  (as  in  general 
the  possibility  of  replacing  those  situated  far  away  from  the 
labor  location  by  similar  deposits  nearer  at  hand)  is  of  course 
a  factor  in  selecting  the  labor  locations.  Locations  which  have 
material  deposits  in  their  neighborhood  and  have  an  opportunity 
to  bring  about  effective  replacements  in  case  of  deviation  will 
eliminate  such  others  as  do  not  have  such  opportunity  precisely 
to  the  extent  to  which  the  attracting  power  of  their  index  0^ 
economy  is  increased  by  economies  of  transportation  costs. ^  A\ 
we  have  seen  from  the  preceding  discussion,  only  the  possibility 
of  replacing  material  deposits  limits  the  real  amount  of  devia 
tion.  It  is  clear  that  such  replacements  influence  the  choice  of  thi 
114  labor  locations,  and  thereby  the  concrete  picture  of  deviation. 
The  general  extent  of  the  deviation  of  the  industry  depen 
upon  its  labor  coefficient.  The  higher  this  coefficient  is,  and 
greater  the  distance  over  which  deviation  takes  place  on  acco 
of  it,  the  greater  will  be  the  distances  which  the  replacemen 
will  cover,  the  more  effective  will  be  the  economies  in  transpo 
and  the  more  will  these  economies  strengthen  the  attract 
power  of  the  labor  locations.  The  attracting  power  of  labor  1 
tions  of  an  industry  will  not  increase  precisely  parallel  to 
labor  coefficient,  on  account  of  the  increasing  replacements;  f 
will  increase  more  than  proportionally.  The  general  rule  thajl 
the  coefficient  of  labor  determines  the  divertibility  of  an  industrll 
may  be  more  exactly  formulated.  Coefficient  of  labor  and  divert: 
bility  of  an  industry  may  be  compared  to  two  rising  lines,  th 

°  Of  course  we  can  calculate  precisely  how  the  attracting  power  of  one  l£ 
bor  location  in  comparison  with  that  of  another  will  be  affected  by  this  poss 
biUty  of  replacement.  We  need  only  compare  the  distances  of  the  labor  locatioi 
from  their  nearest  material  deposits.  By  precisely  the  amount  that  the  distan« 
from  one  labor  location  is  shorter  than  the  distance  from  another,  the  econom 
in  the  case  of  that  labor  location  will  be  greater  than  in  the  other.  A  propo:j 
tionate  amount  is  to  be  added  to  its  index  of  economy. 


rise  of  one  depending  upon  that  of  the  other;  although  the 
rise  of  the  deviation  line  exceeds  that  of  the  labor  coefficient 
line.  We  may  explain  this  fact  by  saying  that  the  divertibility 
is  not  a  phenomenon  simply  parallel  to  the  labor  coefficient,  but 
a  more  complex  functional  phenomenon.  Industries  with  really 
I  high  labor  coefficients  will  therefore  at  the  same  time  be  very 
I  strongly  agglomerated. 


Two  environmental  conditions  of  divertibility  seem  to  be 
quite  accidental  and  to  defy  statements  in  terms  of  a  general 
rule:  the  mutual  distance  between  locational  figures  and  labor 
locations,  and  the  indices  of  economy  of  the  labor  locations.^ 
This  appearance  is  borne  out  by  the  facts  to  a  certain  extent.  For, 
whatever  general  rules  we  may  formulate,  the  actual  situation  of 
a  given  locational  figure  in  relation  to  the  given  labor  locations 
will  always  be  different  for  each  instance,  and  the  actual  per- 
centage of  compression  of  labor  costs  will  remain  a  specific  one 
for  each  location.  From  that,  however,  it  does  not  follow  that 
these  conditions  do  not  take  place  within  the  limits  of  a  general 
Irule,  for  in  fact  they  do.  Both  the  mutual  distance  between  loca-  115 
tional  figures  and  labor  locations  are,  in  general,  dominated  by 
ithe  same  pair  of  internally  interrelated  facts,  the  density  of 
Ipopulation  and  the  level  of  civilization. 

It  is  clear  that  in  sparsely  populated  regions  having  markets 
di  consumption  widely  apart  from  each  other  the  locational 
figures  with  their  minimum  points  will  be  distributed  at  great  in- 
tervals over  the  country;  similarly  "labor  locations"  will  be 
fnore  thinly  scattered  over  the  country  than  in  densely  popu- 
lated regions.  Therefore  the  average  distance  between  the  loca- 
tional figures  and  the  labor  locations  will  be  large.  On  the  other 
land,  a  dense  population  will  mean  that  one  locational  figure 

^  This  statement  involves :  ( i )  the  distance  between  the  locational  figures, 
2)  the  distance  between  the  labor  locations,  (3)  the  distance  between  the  loca- 
ional  figures  and  the  labor  locations. — Editor. 


will  lie  closer  to  another,  one  labor  location  beside  another  labor 
location,  and  hence  that  a  short  average  distance  between  loca- 
tional  figures  and  labor  locations  will  prevail.  The  ranges  of 
deviation  to  be  overcome  will  thus  vary  according  to  the  density 
of  population.  An  increasing  density  of  population  will  always 
mean  that  shorter  distances  have  to  be  overcome,  and  that  there- 
fore more  and  more  favorable  conditions  for  deviation  will  re- 
sult. That  is  the  general  rule  to  which  this  seemingly  accidental 
and  unrelated  point  is  subject. 

With  a  rather  extensive  claim  to  general  validity  we  may 
further  say  that  thinly  populated  regions  will  be  culturally  back- 
ward, or  better,  culturally  "undifferentiated."  The  efficiency  of 
labor  will  not  be  very  different  for  different  locations;  and  like- 
wise the  wages  will  not  vary  greatly.  The  differences  of  labor 
costs  will  hence  be  small  and  their  relative  percentages  of  com- 
pression low.  Vice  versa,  the  differentiation  of  labor  costs  and 
the  relative  percentages  of  compression  of  the  labor  costs  will 
increase  with  an  increasing  density  of  population.  That  is  the 
general  rule  to  which  this  condition  is  subjected. 

Both  together  (the  distances  between  locational  figures  and 
labor  locations,  and  the  indices  of  economy  of  labor  locations) 
will  be  influenced  by  the  density  of  population  and  the  accom- 
panying rise  of  civilization  in  such  a  way  as  to  facilitate  increas- 
ing labor  orientation,  since  increased  percentages  of  compres- 
sion, like  lessened  ranges  of  deviation,  of  course  facilitate  the 
ii6  removal  of  production  to  the  labor  location.  It  may  therefore 
very  well  be  that  in  sparsely  populated  regions  industries  are 
predominantly  oriented  according  to  transportation  facilities,! 
whereas  in  more  thickly  populated  regions  they  are  predomi-i 
nantly  oriented  according  to  labor. 

Finally,  the  significance  of  the  third  environmental  condi-' 
tion,  of  the  transportation  rates,  is  very  simple.  Whenever  the 
rates  per  ton-kilometer  decrease,  the  isodapanes  indicating  devi- 
ation costs  go  farther  apart  and  the  indices  of  economy  of  labor 


locations  are  lowered  proportionately.  As  a  result,  labor  loca- 
tions much  farther  away  will  effectively  attract;  or  in  other 
words,  orientation  according  to  labor  will  influence  a  larger  and 
larger  part  of  the  whole  body  of  industry,  measured  quantitative- 
ly by  units  of  production.  It  will  concentrate  the  production  of 
diverted  industries  more  and  more  at  the  most  advantageous 
labor  locations  by  extending  the  sphere  of  attraction  of  these 
locations.  That  is  the  general  rule  to  which  this  environmental 
condition  is  subjected. 

We  may  look  upon  a  good  part  of  the  struggle  between 
handicraft  and  large-scale  industry  in  the  second  half  of  the 
nineteenth  century  as  a  proof  of  this  rule  concerning  the  results 
;  of  decreasing  transportation  costs.  It  has  already  been  indicated 
!  how  far  the  decline  of  the  handicrafts  means  the  disappearance 
of  production  from  the  markets  of  consumption,  due  to  changes 
j  in  the  material  index  of  the  industries.  Now  we  may  say  that 
:  this  decline  was  hastened  by  the  fact  that  the  railways  facilitated 
the  deviation  of  industry  toward  the  most  favorable  labor  loca- 
tions. Local  differences  of  the  indices  of  labor  costs  (which  had 
been  rather  veiled,  so  to  speak,  by  costs  of  transportation)  be- 
came suddenly  apparent  and  of  practical  significance  when  rail- 
way rates  began  to  decline  rapidly.  Thus  good  labor  locations 
have  collected  around  themselves  large  masses  of  industry  which 
had  formerly  been  oriented  transportationally;  that  is,  had  been 
situated  near  the  market  and  could  therefore  be  organized  on  a 
handicraft  basis.  In  the  second  part  we  shall  show  to  what  in- 
dustries this  applies  particularly.^  But  at  this  time  we  may  ask 
•what  has  removed  products  like  furniture,  baskets,  casks,  etc., 
away  from  the  places  of  consumption  (where  they  used  to  be 
produced  by  handicraft)  toward  the  best  labor  locations  where 

^  As  has  been  pointed  out,  this  second  part  has  never  been  written  by  A. 
Weber;  but  studies  of  individual  industries  by  some  of  his  students  have  been 
published  under  his  direction  by  J.  C.  B.  Mohr,  in  Tübingen.  See  also  Introduc- 
tion.— Editor. 


their  manufacture  takes  place  for  purposes  of  marketing  them 
on  a  large  scale,  though  often  the  conditions  of  manufacture  are 
117  technically  not  greatly  changed.  We  shall  find  that  this  change 
has  been  caused  by  the  lower  transportation  rates. 


All  changes  of  environmental  conditions  have  the  tendency 
to  promote  labor  orientation.  For  the  general  course  of  develop- 
ment is  apparently  in  normal  times  not  only  in  the  direction  of 
decreasing  transportation  costs  but  also  in  the  direction  of  facili- 
tating deviation  by  increasing  the  density  of  population  and  the 
differentiation  of  culture. 

On  the  other  hand,  the  same  technical  developments  which 
diminish  the  costs  of  transportation  change,  pari  passu,  the  gen- 
eral character  of  the  industries  by  mechanizing  the  process  of 
production.  This  decreases  the  labor  coefficient  of  the  industries, 
altering  simultaneously  both  its  factors,  the  amount  of  labor 
used  and  the  amount  of  material  used  per  ton  of  product.  Ob- 
viously, it  increases  the  amount  of  material  used  through  the  use 
of  coal  and  of  weight-losing  materials;  at  the  same  time  it  ren- 
ders manual  labor  superfluous  and  thus  diminishes  the  amount 
of  labor  used.  In  consequence  there  is  less  and  less  labor  neces- 
sary for  a  greater  and  greater  locational  weight.  The  result  is  a 
tendency  continually  to  convert  labor-oriented  industry  into 
transport-oriented  industry.  If  we  wish  by  means  of  our  theory > 
to  make  fully  clear  the  whole  meaning  of  this  tendency  toward! 
integration,  it  can  be  done  by  keeping  in  mind  on  the  one  hand 
the  convergence  of  the  isodapanes  which  is  a  consequence  of  the 
increase  of  the  index  of  materials  and  which  represents  the  ''dif 
ficulty"  of  deviation,  and  by  realizing  on  the  other  hand  how  the» 
decreasing  compressible  quantities  of  labor  costs  per  ton  of 
product  reduce  the  economy  values  of  the  labor  locations,  thus  1. 
pushing  the  critical  isodapanes  of  the  labor  locations  more  close- 1. 
ly  toward  the  minimum  point,  and  again  diminishing  the  possi- 


bility  of  deviation.  If  we  think  of  both  these  things  together,  we 
can  see  that  the  integrating  tendency  which  results  from  the  me- 
chanization of  the  process  of  production  must  be  very  strong.       11 

Whether  it  will  be  stronger  than  the  ^'disintegrating  tend- 
encies" discussed  earlier,  which  also  lie  in  the  historical  develop- 
ment, cannot  be  determined  in  abstracto.  For  only  two  of  the 
opposed  integrating  and  disintegrating  forces  (namely,  the  de- 
creases of  transportation  costs  and  the  increase  of  amount  of 
material  used)  may  be  set  in  relation  to  each  other  abstractly 
and  their  net  effect  evaluated  by  means  of  more  or  less  well- 
known  facts.  For  the  purpose  of  a  provisional  understanding  of 
the  tendencies  of  the  development  as  a  whole  it  will  be  worth 
while  to  investigate  the  relationship  of  these  two. 

An  increase  in  the  use  of  raw  materials  means  an  increase  in 
the  amount  of  weight  which,  in  case  of  a  deviation  from  the 
minimal  point,  must  be  transported.  Decrease  in  the  rates  of 
transportation  means  increase  in  the  amount  which  can  be  trans- 
ported at  the  same  expense.  If  the  amount  of  material  used  by 
an  industry  should  be  doubled,  but  the  rates  of  transportation 
should  be  at  the  same  time  reduced  by  one-half,  the  effects  would 
balance  and  everything  would  remain  as  before  as  far  as  the 
divertibility  of  the  industry  is  concerned.  The  position  of  the 
isodapanes  would  remain  the  same.  The  tendency  to  push  them 
apart  (decreases  in  transport  rates)  and  the  tendency  to  draw 
them  together  (increases  in  the  material  index)  balance  each 
other.  Starting  then  from  this  generalization,  we  may  after  all 
say  something  about  the  total  effect  of  the  integrating  and  dis- 
integrating tendencies  during  the  second  half  of  the  nineteenth 
century.  The  gigantic  cheapening  of  transportation  caused  by 
steam  has  reduced  the  rates  per  ton-kilometer  to  one-fourth, 
one-tenth,  even  one-twentieth  of  what  they  were  formerly.  Now 
there  are  probably  not  many  industries  in  which  the  mechaniza- 
tion of  the  process  of  production  (however  greatly  it  may  have 
expanded  with  the  aid  of  steam)  has  increased  the  weights  to  be 


transported  to  quite  that  extent.  That,  however,  would  have 
been  necessary  in  order  to  balance  completely  the  general  tend- 
ency of  the  isodapanes  to  expand  when  transport  rates  decrease. 
Hence  on  the  whole  they  must  have  been  widened,  for  some  in- 
dustries more,  for  others  less,  according  to  the  extent  of  their 
mechanization,  but  on  the  whole  in  all  industries  to  a  significant 
119  extent. 

From  the  unchecked  widening  of  the  isodapanes  to  four  and 
ten  times  their  extent  (as  was  bound  to  happen  in  all  sections  of 
industry  not  yet  affected  by  mechanization)  we  get  a  picture  of 
the  revolution  in  the  locational  conditions  for  these  even  now 
rather  large  sections  of  industry — a  revolution  due  to  the  enor- 
mously extended  spheres  of  attraction  of  the  labor  locations  in 
them;  and  we  get  a  picture  of  the  extent  to  which,  for  instance, 
the  struggle  between  handicraft  and  manufacturing  industry 
may  be  conceived  simply  as  a  consequence  of  this  increased 
power  of  attraction. 

That  the  widening  of  the  isodapanes  is  impeded  in  those 
industries  which  are  being  mechanized  leads  us  to  the  follow- 
ing considerations:  In  so  far  as  such  widening  occurred — and 
as  we  have  seen,  that  was  predominantly  the  case — a  loosening 
of  industries  and  a  strengthening  of  the  labor  orientation  must 
have  taken  place.  Since,  now,  a  decrease  in  the  indices  of  econ- 
omy of  the  labor  locations  means  a  pushing  of  the  critical  isoda- 
panes toward  the  minimum  points,  we  get  the  following  picture 
applicable  to  the  development  of  the  mechanized  parts  of  indus- 
try: the  isodapanes  are  pushed  apart  (widened)  and  at  the 
same  time  the  critical  isodapanes  are  pushed  back  farther  to- 
ward the  inside  of  the  concentric  rings  formed  by  the  widening 
isodapanes.  Only  in  the  cases  in  which,  as  a  result  of  both  these 
movements,  the  pushed-back  critical  isodapane  was  farther 
from  the  minimal  point  than  it  was  prior  to  the  mechanization 
and  decrease  in  transportation  costs  has  there  been  any  loosen- 
ing up.  It  is  part  of  the  empirical  study  to  show  whether  that 


was  in  fact  the  case  for  large  portions  of  industry,  and  whether 
transport  or  labor  orientation  has  on  the  whole  progressed  far- 
thest, and  furthermore,  which  of  the  two  is  still  progressing  today. 
With  this  final  application  of  these  questions  to  concrete 
reahty  it  is  now  possible  to  take  leave  of  the  laws  of  labor  orien- 
tation so  far  as  pure  theory  is  concerned.  To  determine,  on  the 
basis  of  the  rules  we  have  discovered,  to  what  extent  industry  is 
labor-oriented  and  to  what  extent  transport-oriented  will  be  seen 
to  be  one  of  the  principal  tasks  of  the  study  of  the  empirical  mate- 
rial. It  will  be  evident  that  this  empirical  study  is  one  of  the 
best  means  of  checking  up  the  correctness  of  our  theory  by  an 
appeal  to  the  facts.  For  the  general  criterion  here  set  up  of  the  120 
abihty  of  industry  to  orient  itself  toward  labor,  its  labor  coeffi- 
cient, is  a  clear  characteristic  of  industries,  not  very  difficult 
to  ascertain  in  reality.  It  ought  to  be  possible  to  verify  the  signif- 
icance of  the  labor  coefficient  of  any  industry  for  the  deviation 
of  its  industrial  location  from  the  minimum  points.  121 



Costs  of  transportation  and  costs  of  labor  are  the  only  two 
factors  in  location  which  work  regionally.  All  others  work,  as  we 
have  seen,  only  as  part  of  the  agglomerative  or  deglomerative 
forces  contributing  to  local  accumulation  or  distribution  of  in- 
dustry; and  so  they  operate  only  within  the  general  frameworks 
formed  by  the  regional  factors.  Our  present  task  is  to  introduces 
the  effect  of  these  factors  into  the  general  theory. 



The  first  thing  which  must  be  done  at  this  point  is  to  show- 
that  in  principle  the  theory  does  not  need  to  interpret  agglomera 
tive  and  deglomerative  factors  as  two  groups,  but  as  one  group  ij 
namely,  as  agglomeration.  All  deglomerative  factors  are  by  theii 
very  nature  nothing  but  counter-tendencies  resulting  from  ag 
glomeration.  But  if  that  is  what  they  are,  theory  may  disregard  j 
them  as  independent  factors  and  treat  them  as  the  opposite  o 
agglomeration.   For  the  theory  is  not  concerned  with  the  dy- 
namic interaction  of  operative  tendencies  toward  agglomeratio: 
and  resultant  contrary  tendencies  toward  deglomeration,  bui 
rather  with  the  final  effect  of  this  process,  since  only  this  finaii 
122  effect  alters  the  locational  situation. 

However,  this  final  effect  may  be  that  the  agglomerativ 
tendencies  are  completely  paralyzed  (in  which  case  there  is  nc 
alteration  of  the  locational  picture  we  have  already  gained),  d 
it  may  mean  that  there  is  a  permanent  excess  of  the  tendency  t( 
agglomeration  (in  which  case  theory  has  to  introduce  this  factor 



of  agglomeration  as  one  which  may  possibly  change  our  previ- 
ous picture).  Theory  has,  therefore,  as  a  matter  of  fact  to  deal 
only  with  possible  agglomerations — agglomerations  which  are 
a  resultant  of  complicated  processes. 

Nevertheless  it  would  be  desirable  if  the  abstract  theory 
were  able  to  analyze  into  its  component  parts  the  dynamic  inter- 
action of  agglomerative  and  deglomerative  factors  which  create 
this  ''resultant,"  if  it  were  able  to  dissect  each  group  and  (as  in 
the  cases  of  costs  of  transportation  and  costs  of  labor)  determine 
to  what  degree  each  individual  industry  is  under  the  influence  of 
each  factor. 

Unfortunately  this  cannot  be  done  by  pure  deduction.  Both 
of  the  hitherto  considered  causes  of  location  were  simple  quanti- 
ties which  could  be  deduced  from  the  known  facts  of  some  iso- 
lated industrial  process,  and  their  degree  of  influence  upon  each 
industry  could  also  be  deduced  from  these  facts.  The  groups  of 
locational  factors  now  to  be  considered  are,  on  the  contrary,  dis- 
tinguished by  the  fact  that  they  result  from  the  social  nature  of 
production,  and  are  accordingly  not  to  be  discovered  by  analyz- 
ing an  isolated  process  of  production.  x\nd  in  the  case  of  these 
social  factors  of  concentration  it  is  absolutely  impossible  to  say 
2  priori  whether  production  costs  would  be  lower  or  higher. 
There  is  no  complex  of  known  premises  from  which  such  a  propo- 
rtion could  be  deduced.  We  have  only  empirical  knowledge  of 
individual  facts  to  tell  us  that  certain  elements  of  industry  be- 
:ome  cheapened  in  the  process,  others  more  expensive.  Since  we 
:annot  know  within  the  compass  of  general  theory  the  groups  of 
special  locational  factors  composing  the  agglomerative  and  de- 
!?lomerative  tendencies,  it  is  of  course  impossible  to  discover  by 
leduction  definite  general  diaracteristics  according  to  which  we 
could  determine  the  extent  of  the  influence  of  these  agglomera- 
tive and  deglomerative  factors  upon  the  individual  industries.       123 

Thus  the  task  of  general  theory  is  here  of  necessity  much 
nore  limited  than  in  the  preceding  sections.  Speaking  precisely. 


theory  can  have  only  the  task  of  finding  quite  general  rules  con- 
cerning the  manner  and  extent  of  the  effect  of  the  agglomerative 
tendencies  upon  location;  it  must  rely  upon  empiricism  to  dis- 
cover individual  agglomerative  and  deglomerative  factors  and  to 
apply  the  general  rules  of  agglomeration  to  the  various  indus- 

It  is,  however,  worth  while  to  give  a  certain  foundation  in 
fact  (without  claiming  completeness)  for  our  discussion.  Ac- 
cordingly there  follows  a  short  survey  of  the  more  essential  fac- 
tors known  to  work  in  an  agglomerative  or  deglomerative  man- 
ner. As  the  discussion  proceeds,  it  will  become  clear  that  it  is 
possible  to  make  at  least  a  beginning  of  a  preliminary  grouping 
of  industries,  and  this  as  a  matter  of  pure  theory. 


An  agglomerative  factor,  for  purposes  of  our  discussion, 
an  ''advantage"  or  a  cheapening  of  production  or  marketin| 
which  results  from  the  fact  that  production  is  carried  on  to  some 
considerable  extent  at  one  place,  while  a  deglomerative  factor 
a  cheapening  of  production  which  results  from  the  decent raliza-' 
tion  of  production  (production  in  more  than  one  place).  In  the 
case  of  each  concentrated  industry  the  interaction  of  agglomera- 
tive and  deglomerative  factors  must  always  result  in  certain  in- 
dices of  costs  per  unit  of  product,  indices  which  are  a  function  of 
the  amount  of  concentration.  If  these  indices  of  costs  are  smaller 
in  case  of  great  concentration  than  they  are  in  cases  of  little  con- 
centration, they  clearly  become  for  the  industry  in  question  in- 
dices of  economy.  They  point  out  that  with  a  certain  degree  of 
concentration  the  costs  are  smaller  on  account  of  concentration. 
They  are  smaller  by  a  certain  amount  per  unit  of  product  than 
they  would  be  in  the  case  of  complete  dispersion  of  the  industry, 
or  than  they  would  be  in  a  case  involving  less  concentration. 

We  shall  deal  with  these  indices  of  economy  by  making  use 
of  the  expression  the  function  of  economy  of  agglomeration, 



or  more  briefly  the  junction  of  economy  of  an  industry.  The  124 
expression  function  of  agglomeration  might  be  used  if  it  were 
not  better  to  reserve  this  latter  term  for  another  relation  which 
will  become  important  when  we  try  to  establish  a  precise  arith- 
metical determination  of  the  quantities  of  agglomeration  (cf. 
Appendix  III,  §2). 

The  function  of  economy  is  composed  of  individual  indices 
of  economy  (per  unit  of  product)  which  correspond  to  each  stage 
of  concentration.  If  there  are  several  such  stages  of  concentra- 
tion, each  of  which  results  in  an  additional  saving  in  costs  per 
unit  of  product,  the  industry  has  a  true  function  of  economy.  If, 
on  the  other  hand,  the  saving  results  from  a  particular  definite 
:amount  of  concentration,  and  does  not  continue  to  increase  in 
■case  of  further  concentration,  then  that  industry  has  merely  a 
fixed  index  of  economy  of  agglomeration.  It  is  obvious  that  for 
a  complete  understanding  of  both  these  concepts  the  effect  of 
the  deglomerative  factors  must  be  taken  into  account.  For  the 
present,  in  order  to  explain  the  origin  of  either  this  function  of 
jeconomy  or  this  fixed  index  of  economy,  we  shall  need  to  analyze 
the  various  agglomerative  and  deglomerative  factors. 


A.  Agglomerative  factors,  i .  We  may  in  the  first  place,  as  re- 
gards the  agglomerative  factors,  distinguish  between  two  stages 
bf  agglomeration  at  which  these  factors  are  operative.  The  first 
md  lower  stage  is  that  of  the  concentration  of  industry  through 
he  simple  enlargement  of  plant.  Every  large  plant  with  a  round- 
ed out  organization  represents  necessarily  a  local  concentration 
Ls  compared  with  production  scattered  in  small  workshops  over 
ihe  neighborhood.    The  well-known  economic  advantages  of 
arge-scale  production  as  compared  with  small-scale  production 
n.b.,  not  the  advantages  of  the  large  enterprise  as  compared 
dth  the  small  enterprise ;  we  have  nothing  to  do  with  that)  are 
ffective  local  factors  of  agglomeration.  A  certain  minimum  of 


agglomeration  makes  the  application  of  a  given  technical  appli- 
ance in  the  plant  possible  with  a  certain  percentage  of  saving;  a 
further  minimum  of  agglomeration  makes  possible  a  particular 
form  of  labor  organization  in  the  plant, — this  also  with  a  certain 
125  percentage  of  economy;  and  finally  a  certain  minimum  of  ag- 
glomeration enables  a  plant  to  enter  into  the  economic  relation- 
ship which  makes  possible  cheap  large-scale  purchasing,  cheap  11 
credit,  etc.  These  agglomerative  factors  combined  create  the 
large-scale  plant  of  minimum  efficient  size  for  the  industry  in 
question.  The  coefficient  of  economy  of  the  large  plant  as  com- 
pared with  the  small  (index  of  large-scale  production)  is  also  the 
coefficient  of  agglomeration  of  each  industry,  as  far  as  this  stage 

2.  Whether  an  industry  will  agglomerate  because  of  only 
this  tendency  to  concentration  through  extension  of  plant,  or 
whether  it  will  come  under  the  influence  of  a  further  tendency 
to  concentration,  depends  upon  the  extent  of  the  advantages  re- 
sulting from  close  local  association  of  several  plants.  In  order  to 
get  a  preliminary  systematic  survey  ("preliminary"  I  again  em- 
phasize) of  this  social  agglomeration,  let  it  be  noted  that  thej 
local  aggregation  of  several  plants  simply  carries  farther  the  ad- 
vantages of  the  large  plant,  and  hence  that  the  factors  of  agglom- 
eration which  create  this  higher  stage  of  social  agglomeratioi 
will  be  the  same  as  those  which  created  the  large-scale  plant, 
essential  factors  of  this  higher  stage  of  agglomeration  we  agaii 
list  the  development  of  technical  equipment,  the  development  oi 
labor  organization,  and  a  better  adaptation  to  the  economic  or^j 
ganization  as  a  whole. 

a)  Development  of  the  technical  equipment. — ^The  complet 
technical  equipment  which  is  necessary  to  carry  out  a  process  oif 
production  may  in  highly  developed  industries  become  so  spe-i 
ciaHzed  that  minute  parts  of  the  process  of  production  utilize || 
specialized  machines  and  that  even  quite  large-scale  plants  arej 
not  able  to  make  full  time  use  of  such  equipment.  Such  special-j 



ized  machines  must  then,  together  with  their  own  parts  of  the 
,  process  of  production,  be  taken  out  of  the  single  large  plant  and 
i  must  work  for  several  of  them,  i.e.,  become  the  basis  of  independ- 
ent auxiliary  industries.  In  theory,  the  workshops  of  such  aux-  126 
iliary  industries  may  be  separated  from  the  main  plants  for  which 
they  work,  and  hence  need  not  lead  to  local  concentration  of  the 
j  main  plants.  As  a  matter  of  fact,  however,  they  form  one  tech- 
nical whole  with  the  main  plants  for  which  they  work.  And  this 
,  technical  whole  naturally  functions  best  if  its  mutually  depend- 
ent parts  are  locally  concentrated,  because  then  all  the  parts  re- 
main "in  touch"  with  one  another.  The  development  of  such  spe- 
cialized machines  and  of  the  auxiliary  machines  belonging  to 
them  establishes  therefore  a  technical  minimum  of  agglomera- 
tion, and  this  technical  minimum,  as  soon  as  it  leads  to  a  social 
iconcentration  of  plants,  extends  beyond  the  minimum  of  plants 
previously  considered.  It  thus  becomes  a  factor  of  agglomera- 

And  a  quite  similar  influence  (which  yields  the  same  result) 
lis  exerted  by  a  second  factor  which  we  often  find  adduced  as  a 
pause  of  social  agglomeration,  namely,  the  better  opportunities 
for  replacing  and  repairing  machinery.  The  workshops  for  re- 
placement and  repair  are  a  part  of  the  technical  equipment — in 
1  certain  sense  its  "physician."  The  highly  specialized  develop- 
nent  of  this  aspect  of  production  is  again  possible  only  in  con- 
lection  with  a  large  total  technical  equipment  which  exceeds  the 
;ize  of  a  single  plant.  In  this  case  also  a  scattered  location  of  the 
)lants  which  are  to  be  worked  for,  "country  practice,"  is  pos- 
:.ible ;  but  the  best  and  cheapest  service  is  to  be  secured  "in  town." 
jThe  development  of  these  specialized  technical  functions  accord- 
ngly  becomes  a  factor  of  social  agglomeration. 

b)  Development  of  the  labor  organization. — A  fully  devel- 
)ped,  differentiated,  and  integrated  labor  organization  is  also 
Q  a  certain  sense  equipment.  This  equipment  also  has  parts 
vhich  are  so  specialized  that,  as  a  rule,  they  are  not  adapted  to 



the  conditions  of  a  single  large-scale  plant.  Hence  they  also  tend 
to  form  specialized  auxiliary  or  partial  industries;  and  just  as  in 
the  case  of  the  technical  factors  discussed  before,  these  trades 
based  on  ''division  of  labor"  lend  to  social  agglomeration.  It  is 
127  not  necessary  to  repeat  the  reasons  for  this. 

c)  Marketing  factors. — The  last  group  of  factors — those 
creating  a  more  effective  marketing  situation — ^will  also  be  found 
at  the  stage  of  social  agglomeration.  The  isolated  large-scale 
plant  is  more  effective  than  the  small  one  because  it  can  buy  and 
sell  on  a  large  scale,  thus  eliminating  the  middlemen.  Being  a 
safer  investment,  it  can  get  cheaper  credit.  Grouped  large-scale 
plants  gain  still  further  economies,  especially  in  purchasing  raw 
materials  and  in  marketing.  In  purchasing  raw  materials  the 
concentrated  industry  develops  its  own  market  for  its  materials 
and  from  this  market  it  takes  these  materials  in  the  necessary- 
qualities  and  quantities  at  the  time  of  demand.  The  isolated  en- 
terprise, on  the  other  hand,  is  forced  to  buy  its  materials  in  ad- 
vance and  store  them.  This  means  a  loss  of  interest  for  the  indi- 
vidual enterprise,  and  hence  an  increase  of  money  outlay.  Ir  i 
economic  terms  it  represents  a  wasteful  temporary  tying  up  0: 
capital  which  could  otherwise  be  actively  utilized.  Then  too,  ii 
marketing  the  product,  social  concentration  permits  economies 
because  the  concentrated  industry  produces  a  sort  of  large  uni 
fied  market  for  its  products.  It  is  even  possible  that  the  whol« 
marketing  organization  of  the  manufacturer  can  be  dispensec 
with.  Visits  and  direct  buying  at  the  place  of  production  ma] 
develop,  replacing  the  traveling  salesman.  This  represents,  noi 
only  an  individual,  but  a  general  economic  or  social  saving  m 
well,  since  in  the  process  "labor"  or  social  energy  is  saved. 

d)  General  overhead  costs. — If  for  the  foregoing  and  othej 
reasons  the  best  adaptation  of  industry  to  the  general  economic 
environment  becomes,  at  the  higher  stage  we  are  now  consider 
ing,  a  general  factor  of  agglomeration,  it  should  be  pointed  om 
also  that  the  diminution  of  "general  overhead  costs"  which  plaj 


a  part  at  the  lower  level  of  agglomeration  (i.e.,  in  the  case  of  the 
large  as  compared  with  the  small  plant)  reappear  on  this  stage; 
I  gas,  water  mains,  streets,  the  whole  ''general  apparatus"  will  be- 
come cheaper  for  the  individual  enterprise  at  the  high  level  of 
technical  development  and  effective  utilization  made  possible 
through  social  agglomeration.  128 

To  summarize,  if  for  each  industry  there  is  an  index  of  the 
size  of  the  plant  (be  it  low  or  high  depending  upon  the  condition 
of  technique,  organization,  etc.,  attained  at  any  time)  which  tells 
us  what  unit  costs  per  ton  of  product  correspond  to  each  stage  in 
the  size  of  plant  of  the  industry,  and  which  represents  its  tend- 
ency toward  agglomeration  at  this  lower  stage  of  concentration, 
these  same  factors  will  possibly — they  certainly  frequently  do — 
:arry  the  plant  beyond  this  stage  of  agglomeration. 

Therefrom  a  tendency  to  agglomeration  arises  which  creates 
social  concentrations.  These,  taken  together  with  the  tendencies 
it  the  lower  stage,  determine  the  extent  of  agglomeration  at  this 
second  and  higher  stage  of  agglomeration.  This  may  suffice  as  a 
Dreliminary  survey  of  the  active  factors  of  concentration. 

B.  Deglomerative  factors.  As  we  have  noted,  every  agglom- 
eration may  cause  opposing  tendencies — increased  expenses. 
The  balance  between  the  active  factors  and  these  opposing  tend- 
encies gives  us  the  actual  power  of  agglomeration  effective  in  a 
;iven  case. 

These  opposing  tendencies  result  from  the  size  of  the  ag- 
glomeration as  such;  they  have,  in  contrast  to  the  agglomerative 
actors  which  are  related  to  particular  characteristics  of  each  in- 
dustry, such  as  technique,  level  of  organization,  etc.,  nothing  to 
0  with  these  characteristics.  Their  strength  and  manner  of 
/orking  depends  solely  upon  the  size  of  the  agglomeration.  All 
Igglomerations  of  equal  form  and  size  are  subject  to  them  in  the 
ame  manner.  These  deglomerative  factors  all  follow  from  the 
'se  of  land  values,  which  is  caused  by  the  increase  in  the  de- 
land  for  land,  which  is  an  accompaniment  of  all  agglomeration. 


This  increased  demand  increases  both  the  significance  of  the 
marginal  utihty  of  tracts  of  land  and  the  discounting  of  this  mar- 
ginal utility  by  speculative  manoeuvers.  All  deglomerative  tend- 
encies start  from  the  increase  in  economic  rent  (ground  rent). 
We  can  describe  them  all  as  various  consequences  of  economic 

This  is  not  the  place  to  discuss  through  what  various  means 
all  these  consequences  take  place;  still  less  is  it  the  place  to  dis- 
cuss the  kinds  and  extent  of  the  effects  of  the  various  increasec 
expenses  of  production.  We  are  concerned  only  with  stating  th( 
situation  theoretically.  Developing  further  what  has  alread) 
been  said,  we  have  only  to  note  that  all  these  consequences  rep 
129  resent  merely  a  weakening  of  agglomerative  tendencies.  If  w< 
assume,  for  instance,  that  economic  rent  makes  the  area  0 
land  necessary  for  an  industry  more  expensive,^  that  means  ai 
increase  of  the  general  overhead  costs,  of  whose  diminutioi 
through  agglomeration  we  spoke  earlier.  If  we  assume  that  it  in 
creases  the  costs  of  labor,  it  means  that  part  or  all  of  the  cheap 
ening  of  labor  on  account  of  highly  efficient  organization  will  b 
absorbed.  In  either  case  the  existence  and  increase  of  the  rent  0 
land  means,  not  the  operation  of  fundamentally  new  factors  0 
orientation,  but  alv/ays  only  a  decrease  in  the  effect  of  the  ag 
glomerative  factors.  But  the  growth  of  these  counteracting  el 
fects  will  always  run  parallel  to  the  size  of  agglomeration  as  Ion 
as  the  rent  of  land  parallels  the  size  of  the  agglomeration,  whic 
is  generally  the  case. 

From  the  foregoing  there  follow  the  important  conclusion« 
first,  that  we  may  think  of  the  importance  of  the  deglomerativ 
factors,  even  in  detail,  as  a  weakening  of  the  agglomerative  fac 
tors — a  weakening  which,  appearing  under  certain  circum 
stances,  runs  parallel  to  the  growth  of  agglomeration.  Secondl} 
while  the  factors  of  agglomeration  always  have  application  t 

^  Let  us  assume  also  that  this  increase  in  cost  could  not  be  entirely  avoide 
by  moving  the  industry  to  the  periphery  of  an  agglomeration. 


separate  and  individual  units  of  industry  or  to  one  or  more  con- 
nected branches  of  industry,  the  weakening  of  the  tendencies  to 
agglomeration  (created  by  the  agglomerative  factors  them- 
selves) is  connected  with  only  the  size — size  as  such — of  the  ag- 
glomeration. This  weakening  therefore  comes  into  existence 
even  if  the  agglomeration  is  an  accidental  conglomeration  of  dif- 
jerent  branches  of  industry,  and  it  follows,  since  the  index  of 
economy  resulting  from  agglomeration  is  always  in  part  deter- 
mined by  the  extent  of  the  deglomerative  tendencies  which  are 
it  the  same  time  called  into  being,  that  there  can  exist  theoret- 
'cally  ''pure"  indices  of  economy  in  the  case  of  a  single  agglomer- 
ated industry,  provided  it  is  agglomerated  in  isolation.  But  if  130 
)ther  industries  are  added,  the  resultant  weakening  of  the  ag- 
glomerative factors  and  therefore  the  size  of  the  indices  of  econ- 
omy will  in  part  be  determined  by  the  fortuitous  circumstance 
hat  other  industries  are  also  agglomerating  at  the  same  location. 
Thus  the  theoretically  pure  picture  of  the  orientation  of  an  in- 
iustry  will  be  distorted  by  the  actual  situation  due  to  agglomera- 
ion.  This  alteration  of  reality  we  shall,  following  the  guiding 
)rinciple  of  our  investigation,  for  the  present  leave  out  of  ac- 
:ount.  We  shall  deal  here  with  the  tendency  to  agglomeration  and 
ts  indices  of  economy  as  pure;  more  strictly  speaking,  we  shall 
)roceed  as  if  the  various  industries  did  not  disturb  each  other  as 
he  result  of  the  coincidence  of  their  agglomeration  at  the  same 

From  all  this  it  should  be  clear — and,  through  our  references 
0  reality,  abundantly  clear — in  what  sense  we  shall  speak  of  the 
Jidices  of  economy  due  to  agglomeration  and  of  the  "function  of 
conomy"  as  being  a  composite  of  these  indices  (see  p.  123).  It 
hould  further  be  evident  why  we,  in  abstract  theory,  think  of 
jiis  "function  of  economy"  as  one  whose  single  indices  indicate 
iirther  and  further  economies  per  unit  of  product  as  agglomera- 
on  increases;  and  yet  these  economies  grow  more  and  more 
owly  as  agglomeration  increases.  For  on  the  one  hand  we  have 


the  known  facts  of  experience  in  the  matter,  showing  that  the 
various  agglomerative  factors,  such  as  the  development  of  tech- 
nique, of  organization,  etc.,  in  themselves  all  decrease  progres- 
sively. On  the  other  hand  this  decrease  is  necessarily  accentu- 
ated by  the  weakening  to  which  these  agglomerative  factors  are 
subjected  as  the  rent  of  land  increases  with  the  size  of  the  ag- 
glomeration. Thus  we  may  think  of  the  function  of  economy  as 
one  side  of  a  parabola  which  approaches  more  and  more  slowly 
131  a  maximum  value. 

It  is  hardly  necessary,  I  suppose,  to  explain  more  fully  that 
the  ''fixed  index  of  economy,"  which  knows  only  one  stage  of  ag- 
glomeration and  which  was  on  page  123  introduced  into  the  the- J 
ory,  is  only  a  theoretical  aid,  an  intermediate  assumption  to 
which  no  actual  situation  ever  quite  corresponds.  For  it  is  evi- 
dent that  the  factors  of  agglomeration  with  which  we  have  be- 
come acquainted  will  always  create  a  series  of  stages  (with 
attendant  growing  economies)  which  range  from  the  stage  of  ab- 
solute dispersion  of  location  to  the  theoretical  maximum  of  ag- 
glomeration; and  that  neither  ''absolute  dispersion"  nor  "fixed 
agglomeration  of  a  given  size"  will  ever  exist  in  reality.  The  as- 
sumption of  the  existence  of  this  fixed  agglomeration  will,  how- 
ever, perform  rather  important  auxiliary  services  to  our  theory. 



The  theory  of  agglomeration  deals,  according  to  the  preced-| 
ing  discussion,  with  local  concentrations  of  industry  which  arisi 
because  of  the  fact  that  the  production  of  a  unit  of  product  cai 
in  this  concentrated  producing  complex  be  more  economical! 
performed  by  a  certain  definite  amount.  Hence  the  theory  d 
not  deal  with  those  local  concentrations  of  production  which  a] 
pear  as  the  results  of  other  causes  of  orientation  and  hence  exisi 
quite  independently  of  whether  the  agglomeration  as  such  has 
any  or  no  advantages.  If,  as  is  very  often  the  case,  transportation 


facilities  concentrate  industries  near  the  supplies  of  raw  mate- 
rials, or  at  the  coal  fields,  or  near  the  big  markets  of  consump- 
tion,^ that  phenomenon  does  not  lie  within  the  field  of  the  theory 
of  agglomeration.  The  same  is  the  case  when  the  attracting  "la- 
bor locations"  develop  in  such  a  way  as  to  form  large  centers  of 
agglomeration.^  All  these  are  from  our  present  point  of  view  for- 
'  tuitous  circumstances  in  which  agglomeration  does  not  form  a 
specific  element.  Our  theory  of  agglomeration  has  to  do  only 
with  agglomeration  as  a  necessary  consequence  of  agglomerative 
factors  as  such,  not  as  a  fortuitous  consequence  of  other  causes 
of  orientation;  only  such  part  of  these  other  concentrations  as 
may  be  due  to  independent  agglomerative  tendencies  interests 
us.  Hence  that  agglomeration  with  which  the  theory  will  deal  132 
will  be  called  "pure"  or  "technical,"  thus  contrasting  it  with  ag- 
glomeration which  is  incidental  to  other  forces. 


The  tendency  to  agglomeration  for  technical  reasons  may 
i  first  be  considered  in  its  effect  upon  production  which  is  oriented 

solely  with  regard  to  transportation  and  not  diverted  to  "labor 
!  locations."  What  effect  would  a  tendency  to  agglomeration  with 

a  fixed  index  have  in  this  case? 


Assuming  for  the  present  that  the  agglomeration  is  a  case  of 
,only  one  unit  with  a  perfectly  definite  economy,  let  us  put  two 
questions :  When  will  agglomeration  take  place,  and  to  what  ex- 
'tent?  And,  if  it  does  take  place,  where  will  it  take  place? 

a)  When  does  agglomeration  take  place,  and  how  much? — 
By  means  of  the  concepts  of  minimum  points  and  isodapanes  as 
they  have  been  used  earlier  it  is  very  easy  to  develop  the  answer 
to  this  question.  It  is  only  necessary  to  recall  what  was  said 
about  the  indices  of  economy  of  the  labor  locations  and  their  ef- 

See  above,  p.  71.  ^  Cf.  above,  p.  112. 



feet.  The  centers  of  agglomeration  also  form,  with  regard  to 
scattered  production,  centers  of  attraction  having  particular  in- 
dices of  economy.  If  production  moves  to  these  centers,  that  fact 
signifies  a  deviation  accompanied  by  transportation  costs  higher 
than  those  of  production  located  at  the  points  of  minimum  trans- 
portation cost.  And  naturally  this  deviation  depends  fundamen- 
tally on  the  same  conditions  as  those  set  forth  on  pp.  112  ff.  The 
deviation  costs  per  ton  of  product  must  be  smaller  than  the  econ- 
omies per  ton  of  product.  These  economies  per  ton  of  product 
are  indicated  by  the  index  of  economy  of  the  unit  of  agglomera- 
tion. The  isodapanes  indicate  the  deviation  costs  per  ton  of 
product.  For  every  individual  part  or  unit  of  the  production 
complex  there  must  be  a  critical  isodapane  the  deviation  cost  in- 
dex of  which  corresponds  exactly  to  the  index  of  economy  of  the 
unit  of  agglomeration. 

If  that  is  clearly  understood  we  can  at  once  see  that  individ- 
ual units  of  production  become  agglomerated  and  give  rise  to 
centers  of  agglomeration  if  their  critical  isodapanes  intersect,  and 
if  the  quantity  of  production  of  each  individual  unit  added  to 
that  of  the  other  units  which  participate  in  the  same  overlapping 
segment  reaches  the  effective  unit  of  agglomeration.  For  if  such 
critical  isodapanes  intersect,  then  for  the  various  individual  units 
some  common  points  exist  at  which  the  economy  of  agglomera- 
133  tion  is  not  absorbed  by  the  deviation  costs.  And  when  the  quan- 
tity of  production  which  can  be  concentrated  at  that  point  reach- 
es the  assumed  unit  of  agglomeration,  then  the  agglomeration 
pays ;  it  can  be  effectively  realized.  To  state  it  precisely,  the  for- 
mation of  centers  of  agglomeration  and  the  agglomeration  of  in-i 
dividual  units  of  production  at  these  centers  depends  upon  two! 
circumstances:  first,  upon  the  existence  of  intersections  of  crit- 
ical isodapanes  in  relation  to  the  assumed  unit  of  agglomeration, 
and  second,  upon  the  attainment  of  the  requisite  quantity  of 
production  within  these  segments.  When  these  two  conditions 
are  fulfilled,  the  individual  units  of  production  become  agglom- 



erated  and  the  concentration  affects  all  parts  of  the  production 
complex.  Whatever  the  situation  and  whatever  the  quantity  of 
output  of  any  indivdiual  unit,  if  its  critical  isodapanes  intersect 
with  those  of  enough  other  individual  units  to  make  up  a  unit  of 
agglomeration,  it  will  be  concentrated  with  these  others. 

For  a  clarification  of  the  two  "conditions"  it  is  necessary  to 
note  the  following,  which  again  is  in  part  analogous  to  the  case  of 
orientation  as  affected  by  labor.  Theoretically,  only  those  pro- 
ductive units  can  be  brought  together  in  the  case  of  each  of  which 
the  economies  relating  to  its  particular  quantity  of  production 
exceed  the  deviation  costs,  since  only  for  such  units  does  the 
overlapping  segment  exist.  In  fact,  however,  the  agglomeration 
can  (for  the  purpose  of  attaining  the  requisite  amount  of  pro- 
duction) somewhat  exceed  this  theoretical  Hmit  and  can  also  at- 
tract certain  productive  units  which  are  somewhat  farther  away 
and  whose  critical  isodapanes  do  not  quite  reach  the  segment. 
This  may  happen  if  the  ratio  of  economies  to  deviation  costs  for 
other  parts  of  the  agglomeration  is  so  favorable  that  a  balance  on 
the  side  of  economy  still  remains  for  the  agglomerated  industry 
as  a  whole,  even  though  a  part  of  the  economies  arising  from 
agglomeration  must  be  applied  to  covering  the  negative  balance 
between  economies  and  deviation  costs  of  such  '^fragments";  for 
in  such  a  case  the  attraction  of  the  ''fragments"  will  cause  lower 
costs  for  the  group  as  a  whole.  Beyond  such  occasional  supple- 
menting of  units  of  agglomeration  which  are  not  quite  complete, 
agglomeration  cannot  and  will  not  go;  because,  as  will  be  shown  134 
later,  the  "effective  unit  of  agglomeration"  roughly  forms  the 
upper  limit  of  agglomeration.  Only  by  throwing  together  many 
units  of  agglomeration  could  a  "surplus"  be  created  sufficient  to 
attract  on  a  large  scale  productive  units  whose  isodapanes  do  not 
reach  the  segment.  Thus  this  whole  matter  of  agglomeration  of 
units  which  lie  too  far  away  when  considered  by  themselves 
means  no  great  alteration — only  a  comparatively  insignificant 
modification — of  the  two  conditions  upon  which  agglomeration 



depends;  the  basic  proposition  still  holds  that  a  unit  of  agglom- 
eration with  a  given  index  will  bring  together  all  those  parts  of  a 
total  industry  whose  critical  isodapanes  as  worked  out  in  terms 
of  this  unit  intersect  with  each  other,  if  the  combined  or  concen- 
trated production  of  these  parts  is  sufficient  to  make  up  the  ef- 
fective unit  of  agglomeration. 

b)  Where  will  agglomeration  take  place? — And  where  will 
the  center  of  agglomeration  lie?  That  also  is  easily  made  clear 
by  means  of  the  isodapanes.  The  center  of  agglomeration  must 
obviously  lie  within  the  common  segments  of  the  critical  isoda- 
panes, for  within  these  common  segments  He  the  points  at  which 
production  may  be  concentrated  without  prohibitive  deviation 
costs.  Every  point  within  a  common  segment  is  a  possible  point 
of  agglomeration;  for  at  any  such  point  production  under  ag- 
glomerated conditions  can  take  place  more  cheaply  than  at  the 
scattered  points  of  minimum  transportation  costs.  But  where 
will  the  center  of  agglomeration  actually  be  located?  It  will  be 
located  at  that  one  of  the  several  possible  points  of  agglomera- 
tion which  has  the  lowest  transportation  costs  in  relation  to  the 
total  agglomerated  output.  (See  Fig.  20.) 

The  various  units  going  into  the  agglomeration  have  outputs 
or  production  of  varying  size,  and  the  diversion  of  a  large  quan-  ( 
tity  of  output  toward  a  point  of  agglomeration  involves  greater 
transportation  costs  than  does  the  diversion  of  a  small  quantity 
135  of  output.  Within  the  common  segments  the  agglomeration  will 
become  so  situated  that  the  larger  units  of  production  have 
changed  their  positions  less  than  have  the  smaller  ones,  for  this 
will  keep  down  the  total  deviation  costs.  Stated  in  other  words, 
the  large  units  of  production  will  attract  the  smaller  units  to  loca- 
tions near  the  former's  original  minimum  points,  and  will  there 
fix  the  center  of  agglomeration. 

We  can  state  the  result  of  this  dynamic  process  with  great 
precision  in  the  following  manner :  All  the  agglomerated  produc-  ■ 
tive  units,  together  with  their  common  location  of  production ' 


(the  center  of  agglomeration),  constitute  one  great  locational 
figure  of  the  type  which  is  already  familiar  to  us.  Its  corners  are 
the  various  raw-material  supplies  and  markets  of  the  various 
constituent  units.  The  position  of  the  location  in  this  figure  will 
be  determined  by  the  components  of  the  different  corners  pre- 
cisely in  accordance  with  the  laws  of  those  locational  figures 
which  have  already  been  studied.  The  precise  location  of  the 
center  of  agglomeration  will  thus  be  that  of  the  minimum  point 
of  transportation  cost  for  this  locational  figure.  It  must  lie  with- 

FiG.  20  Fig.  21 

in  the  segment  of  the  isodapanes,  and  within  this  segment  it  may 
be  quite  definitely  located. 

c)  The  size  of  the  unit  of  agglomeration. — Hard  upon  the 
heels  of  the  solution  of  the  question  as  to  the  point  at  which  the 
production  in  a  given  segment  takes  place  there  follows  the  prob- 
lem as  to  which  of  several  possible  agglomerations  a  unit  of  pro- 
duction will  choose;  and  this  leads  to  the  important  rule  already 
indicated  concerning  the  size  of  centers  of  agglomeration.  If  the 
isodapanes  of  an  individual  unit  of  production  intersect  in  sev- 
eral areas  and  in  several  directions  with  those  of  other  individual 
units — that  is,  if  an  individual  unit  has  several  possibilities  of 
agglomeration,  it  will  agglomerate  within  that  common  segment 
in  which  the  center  of  agglomeration  is  least  distant  from  the 
former  minimum  point  of  the  individual  unit  concerned.   For 


thus  the  smallest  additional  transportation  costs  and  the  largest 
136  surplus  from  the  index  of  economy  will  result.  In  this  connection 
it  should  be  noted  that  the  point  of  agglomeration  is  more  likely 
to  be  fairly  near  to  the  particular  unit  concerned  when  the  other 
individual  units  are  situated  close  at  hand,  so  that  the  segments 
formed  by  the  intersections  of  the  critical  isodapanes  are  large. 
For  illustration  compare  Figure  21.  The  actual  location,  how- 
ever, within  the  segments  still  depends  upon  the  relative  size 
of  the  quantities  of  production  concerned,  as  was  shown  in  our 
previous  discussion.  In  consequence,  even  though  each  indi- 
vidual unit  tends  to  choose  the  largest  possible  segment  (i.e., 
agglomerates  with  the  other  units  nearest  to  it),  it  will  also  tend 
to  choose  the  particular  segment  within  which  the  point  of  ag- 
glomeration is  nearest  to  it.  Among  the  segments  in  its  vicinitj 
it  will  choose  the  one  in  the  case  of  which  the  smallest  possible 
additional  quantity  of  production  still  suffices  for  the  unit  of  ag- 
glomeration which  has  to  be  gotten  together.  Put  in  a  slightl> 
different  way,  and  using  terribly  cumbersome  abstract  terminol- 
ogy (which  unfortunately  is  nevertheless  hardly  adequate  to  ex 
press  these  matters),  we  might  say:  the  isolated  units  of  produc 
tion  will  not  agglomerate  arbitrarily  or  indifferently  with  any  0: 
the  others  near  them;  but  rather  they  will  agglomerate  witl' 
those  smallest  units  which  just  suffice  to  make  up  a  requisite  unr 
of  agglomeration,  and  which  they  can  attract  farthest  to  them- 
selves, attracting  first  the  smaller  ones  and  then  going  upward  irl 
the  scale  to  the  larger  ones. 

This  is  the  theorem  which  provides  the  promised  insight  int 
the  fundamental  nature  of  this  kind  of  orientation.  From  th 
fact  that  each  individual  unit  in  the  process  of  concentratior 
selects  from  those  others  lying  near  it  the  smallest  which  will  suf 
fice  for  a  unit  of  agglomeration,  there  follows  as  a  general  featun 
of  agglomeration  the  tendency  not  to  exceed  the  size  of  a  requi 
site  unit  of  agglomeration,  and  hence  the  tendency  to  concentrate 
in  as  many  centers  as  there  exist  requisite  units  of  agglomera 




tion.  This  result  may  also  be  reached  by  showing  that  each  ag- 
glomeration means  a  deviation  with  resultant  costs;  and  the 
deviation  which  occasions  these  costs  will  not  be  carried  farther 
than  to  form  units  which  just  offset  these  costs.  However,  it  is 
important  further  to  demonstrate  this  by  making  use  of  an  exact 
and  detailed  analysis  of  the  formation  of  the  individual  centers 
of  agglomeration. 

d)  Modifications. — We  must  now  (again  in  strict  accord- 
ance with  our  discussion  of  the  attraction  of  labor  locations)  in- 
troduce the  modification  of  the  power  of  attraction  of  the  centers 



Fig.  22 

)f  agglomeration  resulting  from  the  elimination  of  material  de- 
Dosits.  This  modification  must  be  made  because  of  the  fact  that 
n  drawing  together  at  one  place  several  units  of  production  more 
ind  less  favorable  deposits  of  supply  will  result  for  each  kind  of 
naterial  used,  the  respective  advantages  of  these  deposits  de- 
)ending  upon  the  relation  of  the  supplies  which  were  formerly 
ised  by  the  isolated  units  to  the  new  site  of  production.  It  fol- 
ows  that,  as  in  the  case  of  the  "labor  locations,"  the  unfavorable 
deposits  will  be  eliminated  (as  in  Fig.  22  above,  M\  and  M2) 
nd  the  supply  will  (assuming  sufficient  productivity)  be  limited 
p  the  most  favorable  deposits  of  each  kind  of  material. 

In  addition  to  this  change,  which  will  take  place  regularly, 
;  may  also  happen  that  the  place  of  agglomeration  is  by  chance 
ituated  in  the  neighborhood  of  a  material  deposit  which  has  not, 


up  to  this  time,  been  used.  Then  this  new  deposit  will  be  substi- 
tuted (in  place  of  all  others  of  the  same  kind  of  material  former- 
ly used),  since  it  is  most  favorable  for  the  new  conditions  of 
production.  Compare  Figure  23.  Here  M\  is  eliminated  as  less 
favorable  than  Mi ;  but  so  also  are  M2  and  M'2  eliminated,  since 
138  both  are  less  favorable  than  the  new  deposit  ikf'a- 

Both  these  circumstances  will,  by  saving  transportation  costs, 
strengthen  the  power  of  attraction  of  the  centers  of  agglomera- 
tion by  a  certain  amount  which  should  be  added  to  their  index  of 
economy,  an  addition  which  must  be  the  larger  the  farther  the  at- 
traction of  the  original  index  of  economy  happens  to  extend,  with 
the  result  that  more  distant  units  are  attracted  and  the  differen- 
tial advantage  between  the  unfavorable  sources  of  material  elim- 
inated and  the  favorable  ones  brought  into  use  is  greater.  All  this 
is  similar  to  what  we  found  in  the  case  of  labor  location. 

But  while  the  position  of  the  attracting  labor  location  is  nol ' 
changed  by  ehminating  certain  deposits  of  material  (since  this 
labor  location  is  definitely  fixed),  the  effect  of  this  eliminating j 
process  goes  farther  in  the  case  of  agglomeration.  In  the  lattei 
case  the  geographical  position  of  the  attracting  place  of  agglom- 
eration is  affected,  since  this  position  itself  depends  (within  the 
segments  of  the  isodapanes)  upon  the  locational  figures  them- 
selves. If  parts  of  these  locational  figures  cease  to  operate  ae 
effective  determinants,  the  whole  basis  of  orientation  will  be 
changed.  But  it  may  be  stated  at  once  that  it  is  very  easy  to  de- 
termine the  new  position,  and  that  the  separation  from  the  olc 
basis  is  not  complete;  the  old  deposits  still  continue  to  effect 
potentially,  and  in  a  definite  direction,  the  process  of  agglomera- 
tion. This  last  point  is  obvious;  for  the  new  deposits  might  be- 
come exhausted,  and  then  it  would  be  necessary  to  resort  to  thf 
old  ones. 

Speaking  of  the  new  position,  then,  (i)  the  centers  of  con- 
sumption which  are  to  be  served  from  this  point  of  agglomera- 
tion and  (2 )  the  sources  of  materials  which  remain  in  use  are  the 


only  factors  which  need  to  be  considered  as  the  basis  of  a  new 
locational  figure  with  the  corresponding  component  weights  in 
order  to  see  where  the  point  of  agglomeration  will  lie;  it  will  sim- 
ply be  the  minimum  point  of  the  new  locational  figure,  according 
to  the  laws  familiar  to  us.  In  Figure  22,  A  is  the  minimum  point 
of  C'Mi  CM' 2]  in  Figure  2^,  A  is  the  minimum  point  of  C'Mi, 
CM'' 2.  As  is  evident  at  once,  the  point  of  agglomeration  will  gen- 
erally remain  in  the  neighborhood  of  the  selected  material  de- 
posits. For  numerous  and  divided  markets  which  have  a  rela- 
tively weak  attracting  force  will  pull  against  material  deposits 
whose  weight  is  concentrated  upon  a  few  strong  ropes  (using  the 
terms  known  to  us  from  our  Varignon  apparatus).  In  addition,  139 
these  markets  will  mutually  paralyze  each  other  on  account  of 

Fig,  24 

their  necessarily  opposed  positions.  Consequently,  the  original 
position  of  the  point  of  agglomeration  in  the  neighborhood  of 
these  (new)  deposits  will  be  retained,  or  at  any  rate  will  not  be 
greatly  changed. 


Now  to  turn  to  the  usual  case  that,  for  the  unit  in  question, 
:here  is  not  only  a  saving  for  a  certain  given  unit  of  agglomera- 
ion,  but  there  exists  also  a  function  of  economy  because  econ- 
omies continue  to  rise,  increasing  while  the  size  of  agglomerations 
•ncreases.  Such  a  function  of  economy  is  in  point  of  fact  made 
ip  entirely  of  single  units  of  agglomeration,  each  one  having  a 
Darticular  index  of  economy.  The  effects  (on  the  distributed  or 
scattered  industry)  of  the  tendency  to  agglomeration  can  be 
nade  clear  if  one  imagines  this  tendency  to  agglomeration  as  be- 
ng  the  concurrent  effects  of  all  these  various  units  of  agglomera- 
ion  with  their  different  indices.  Each  of  these  units  will  bring 



together  the  parts  of  the  scattered  industry  according  to  the  ex- 
tent of  its  agglomerative  power,  following  the  laws  with  which 
we  have  become  acquainted.  Hence  we  can  think  of  their  com- 
mon effect  as  a  competition  of  the  various  units  of  agglomeration 
with  respect  to  the  form  of  the  agglomeration;  while  within  each 
of  the  struggling  units  the  agglomeration  takes  place  according 
to  the  rules  which  have  already  been  developed.  The  question  as 
to  the  effect  of  a  function  of  economy  composed  of  the  units  a^  a-, 
as,  etc.,  is  simply:  toward  which  of  these  units  will  the  agglomer- 
ation take  place?  After  that  question  has  been  decided  all  the 
rest  takes  place  according  to  the  rules  already  set  forth. 

Fig.  25  Fig.  26 

Which  unit  of  agglomeration  will  win  out  may  be  deduced 
rather  simply  from  the  standpoint  of  the  individual  units  of  pro- 
duction affected.  Around  the  minimal  point  of  each  individual 
unit  of  production  extend  critical  isodapanes  which  corresponc 
to  the  index  of  economy  of  each  unit  of  agglomeration.  The 
critical  isodapanes  of  the  higher  units  with  higher  indices  oi 
140  economy  will  lie  more  distant  than  those  of  the  lower  units;  ir 
our  example  «2  will  lie  more  distant  than  Gi,  a^  more  distant  thar 
fls,  etc.  How  this  works  is  indicated  for  a  function  with  two  units 
01  and  02  in  the  figures  below  (25-28).  The  critical  isodapanes  ol 
higher  units  are  hkely  to  intersect  with  more  isodapanes  of  othei 
isolated  units  than  is  true  of  the  smaller  units.  However,  these 


higher  units  also  need  larger  masses  of  production  in  order  to 
come  into  operation;  they  must  bring  together  a  larger  number 
of  isolated  units  of  production.  And  these  higher  units  will  come 
into  competition  with  the  smaller  units.  This  may  best  be  made 
clear  by  the  simple  example  of  two  units  of  agglomeration  (öi 
and  Ö2)  competing. 

The  isodapanes  of  higher  rank  (represented  in  our  example 
by  ßo)  may  not  bring  together  a  larger  number  of  productive 
units  than  do  the  lower  ones,  because  these  isodapanes  are  drawn 

Fig.  27  Fig.  28 

iround  the  minimum  points  at  so  small  an  additional  distance 

:rom  the  lower  ones  that  they  do  not  have  segments  in  common 

vith  any  more  units  than  do  those  lower  ones  (Fig.  25).  In  that 

:ase  the  higher  units  of  agglomeration  will  not  be  able  to  com- 

)ete  with  the  lower  units.  Or  it  may  be  that  the  isodapanes  of  141 

ligher  rank  actually  include  within  their  segments  a  larger  num- 

)er  of  productive  units  (Fig.  2  6,  where  02  includes  three,  and  Fig. 

7,  where  a-,  includes  four,  units,  while  öi  only  includes  two  in 

ach  case).  Assuming  that  a  quantity  of  production  sufficient 

or  agglomeration  is  present,  there  will  be  competition  between 

he  two  units  of  agglomeration.  The  outcome  of  this  competition 

rill  depend  upon  whether  the  ratio  between  the  economies  of 

gglomeration  and  additional  costs  of  transportation  is  more  fa- 

orable  in  the  case  of  agglomeration  toward  Ci  than  it  is  in  the 


case  of  agglomeration  toward  02-^  This  ratio  is  accurately  ex- 
pressed by  the  distance  between  the  isodapane  on  which  the 
place  of  agglomeration  for  the  unit  in  question  will  actually  lie, 
and  the  critical  isodapane  belonging  to  this  same  unit.  It  will  be 
remembered  that  the  critical  isodapane  indicates  the  extent  to 
which  economies  can  be  gained  by  means  of  agglomeration  to- 
ward this  unit.  The  isodapane  on  which  the  place  of  agglomera- 
tion will  actually  lie  indicates  the  actual  additional  transporta- 
tion costs  which  will  have  to  be  assumed  in  order  to  effect  this 
particular  agglomeration.  The  greater  the  difference  between 
these  necessary  additional  costs  and  the  actual  economies,  the 
more  favorable  the  situation  for  agglomeration.  Hence  it  is  only 
necessary  (i)  to  examine  from  the  standpoint  of  the  individual 
units  of  production  the  common  segments  of  the  critical  isoda- 
pane of  the  different  units  (in  our  case  the  segments  of  02  and 
öl)  and  (2)  to  ascertain  in  which  of  these  segments  the  distance 
between  the  points  of  agglomeration  and  the  critical  isodapanes 
will  be  greatest  in  order  to  know  in  which  segments  the  agglom- 
eration will  take  place.  Assuming  for  the  time  being  equally 
large  productive  units  (which  will  place  the  points  of  agglomera- 
tion at  the  center  of  the  segment),  it  follows  that  the  distance 
between  the  points  of  agglomeration  and  th,e  critical  isodapanes 
142  will  increase  in  proportion  to  the  size  of  the  segments.  It  is,  then, 
only  necessary  to  look  at  the  size  of  the  segments  in  order  tc 
know  toward  which  units  the  agglomeration  will  take  place,  as- 
suming that  sufficient  quantities  of  production  are  available  for 
the  segments  of  all  the  units.  In  Figure  26  agglomeration  will 
take  place  toward  d ;  for,  although  it  seems  at  a  first  glance  pos- 
sible that  agglomeration  might  go  toward  the  higher  unit  (^2),  it 
will  not  do  so  because  the  segments  of  the  lower  unit  are  larger; 
they  show  greater  distances  between  the  point  of  agglomeratioDJ 
and  the  critical  isodapanes,  and  hence  have  greater  actual  econ^ 
omies.  But  when,  as  in  Figure  27,  isodapanes  of  higher  rank  lit 

*  The  text  in  the  preceding  paragraph  has  been  rewritten. — Editor. 


so  far  beyond  those  of  lower  rank  that  not  only  do  these  higher 
isodapanes  include  within  their  segments  more  production  (and 
sufficient  production  to  make  up  the  greater  total  quantity  re- 
quired for  the  higher  unit),  but  also  their  segments  are  larger 
than  those  of  the  isodapanes  of  lower  order,  then  in  that  case  the 
higher  unit  of  agglomeration  will  win  out. 

To  sum  up  the  argument  in  general  terms:  the  agglomera- 
tion of  higher  rank  will  eliminate  the  agglomeration  of  lower 
rank  only  when  the  isodapanes  of  higher  rank  surround  the  min- 
imum point  at  a  distance  so  much  greater  that  they  not  only  ( i ) 
gather  within  their  segments  the  amount  of  production  required 
for  the  agglomeration  of  higher  rank,  but  also  (2)  form  larger 
segments  and  hence  offer  more  favorable  points  of  agglomeration 
for  the  individual  units  of  production  than  do  the  segments  of 
the  critical  isodapanes  of  lower  rank. 

It  may,  of  course,  be  that  only  the  critical  isodapanes  of  ag- 
glomerative  units  of  higher  rank  form  segments,  while  those  of 
lower  rank  do  not  touch  each  other  at  all  (compare  Fig.  28).  In 
this  case  the  agglomeration  of  lower  rank  will  be  unable  to  com- 
pete. This  case  is  diametrically  opposite  to  that  first  discussed. 
In  this  latter  case  the  isodapanes  of  higher  rank  surround  the 
minimum  points  at  much  greater  distances  than  do  those  of  the 
lower  rank  which  cling  closely  to  the  minimum  points. 


From  the  foregoing  discussion  one  condition  on  which  the 
form  of  the  agglomeration  depends  should  have  become  clear.  It  143 
is  the  manner  in  which  the  critical  isodapanes  of  the  various 
units  follow  each  other.  According  to  the  previous  analysis,  close 
succession  of  critical  isodapanes  indicates  that  agglomeration 
will  move  toward  an  agglomerative  unit  of  lower  rank;  whereas 
wide  separation  indicates  that  it  will  move  toward  a  unit  of  high- 
er rank;  hence  agglomeration  depends  first  on  the  scale  of  the 
isodapanes.  This  scale  presents  a  graphical  picture  of  the  rate 



at  which  the  economies  increase  with  successive  units  of  agglom- 
eration. It  is  a  diagram  of  the  increase  of  the  function  of  econ- 
omy— a  diagram  projected  upon  a  horizontal  surface  (compare 
illustration  below,  Figs.  29  and  30).  If  the  indices  of  econ- 
omy per  ton  of  product  increase  rapidly  as  the  agglomerative 
units  increase,  then  the  corresponding  isodapanes  (cf.  a^,  a.z,  a^ 
in  Fig.  29)  are  far  apart.  Vice  versa,  if  these  indices  increase 
slowly,  the  isodapanes  are  close  together  (cf.  a^,  Go,  Ö3,  in  Fig. 
30).  The  preceding  analysis  is  thus  nothing  but  an  exact  formu- 

Aj  A2  A3 
Fig.  29 

Aj    As   Ag 
Fig.  30 

lation  of  the  fact  that  (and  in  what  manner)  the  size  of  the  ag 
glomeration  will  be  dependent  on  the  rapid  or  slow  increase  0 
the  function  of  economy.  It  shows  in  what  manner  the  functioi 
of  economy  represents  the  first  factor  influencing  agglomeratioi 
by  determining  the  number  and  size  of  the  units  of  agglomer 

But  on  closer  examination  it  shows  also  what  additional  fao 
tors  are  concerned.  Apart  from  the  succession  of  the  isodapanes 
evidently  three  other  factors  must  be  taken  into  consideration! 

First,  The  distance  according  to  which  the  critical  isodz 
panes  are  fundamentally  spaced  is  to  be  clearly  understood  a 
something  different  from  their  succession  in  the  scale.  A  give: 
succession  of  critical  isodapanes  may  be  spread  over  a  widely  ex 
tended  circular  formation  or  over  a  narrow  funnel  of  isodapanesj 
according  to  whether  their  basic  spacing  interval  is  large  or  small 
(cf.  the  figures  of  the  Appendix,  p.  241  f.).  And  each  will  necest 


sarily  have  its  own  significance  for  the  agglomeration.  We  shall 
Dresently  discuss  that  aspect  of  the  matter.  144 

Second,  The  physical  distance  of  the  units  of  production.  If 
they  are  spread  widely  apart,  scattered  about  the  country,  the 
Dossibility  of  forming  common  segments  of  their  isodapanes  will 
De  less  than  if  these  industries  were  already  close  together. 

Third,  The  quantity  of  production  of  the  units  of  produc- 
:ion.  On  this  depends  the  magnitude  of  the  masses  of  production 
vhich  are  to  be  agglomerated  within  the  segments,  and  this  cir- 
:umstance  determines  which  of  the  different  segments,  if  any, 
lave  access  to  quantities  of  production  sufficient  for  their  ag- 
jlomerative  units. 

In  analyzing  these  three  factors  further,  the  following  ob- 
;ervations  may  be  made. 

We  are  already  acquainted  with  the  first  factor  from  our  dis- 
;ussion  of  labor  orientation.  We  there  found  that  the  basic  dis- 
ance  of  the  isodapanes  is  determined  (i)  by  the  locational 
veight  of  the  industry  (a  condition  implicit  in  its  character) ,  and 
2)  by  the  general  rates  of  transportation  (a  general  environ- 
nental  condition).  This  first  factor,  therefore,  may  be  sepa- 
ated  into  two  conditions  which  work  independently  of  each 

On  the  other  hand,  the  second  and  third  factors  may  be  com- 
>ined,  since  they  depend  upon  one  single  condition,  that  of  the 
lensity  of  industry.  For  the  quantity  of  production  of  the  sev- 
ral  units  of  production,  taken  together  with  their  distance  from 
ach  other,  constitute  the  density  of  industry  relative  to  a  given 
.rea.  It  is  useful  to  combine  these  two  concepts  into  the  one  con- 
ept  of  the  density  of  industry,  since  both  in  reality  are  a  reflec- 
ion  of  the  same  general  environmental  condition,  the  density  of 
'opulation.  Density  of  population  empirically  has  these  two  as- 
•ects:  (i)  density  of  the  population  of  a  particular  locanty= 
[uantity  of  production  of  the  units  of  production;  (2)  number 



of  centers  of  population = distribution  of  the  individual  units  of 

As  in  the  case  of  labor  orientation,  we  find  two  conditions  in- 
herent in  the  character  of  the  industry,  and  on  these  two  condi- 
tions the  deviation  to  centers  of  agglomeration  depends :  ( i )  the 
junction  of  economy  of  the  industry  and  (2)  its  locational 
weight.  So  also  we  have  two  environmental  conditions :  the  costs 
of  transportation  and  the  density  of  industry  (or,  as  we  may  say 
empirically,  the  density  of  population) .  These  are  the  same  en 
145  vironmental  conditions  as  those  influencing  labor  orientation. 

Let  us  now  first  examine  more  closely  the  nature  of  the  influ- 
ence of  the  locational  weight  and  of  the  two  environmental  con- 
ditions, and  second,  work  out  at  least  a  general  picture  of  ag- 
glomeration under  the  combined  influence  of  all  the  conditions j 

It  will  probably  not  be  necessary  to  restate  the  general  way] 
in  which  the  locational  weight  and  the  transportation  costs  worL 
It  will  be  remembered  that  if  both  decrease,  the  isodapane  will 
expand;  if  both  increase,  the  isodapane  will  tend  to  contract — 
in  other  words,  both  factors  work  alike.  It  is  more  important  to 
realize  that  one  of  the  two  factors  upon  which  the  density  of  m-\ 
dustry  depends,  namely,  the  distance  of  the  individual  units  0) 
production,  has  the  same  effect.  The  expansion  or  contractioi 
of  the  isodapanes  (without  altering  their  order  in  the  scale,  to  be 
sure)  as  caused  by  a  change  of  locational  weight  and  a  change  ol 
transportation  costs  (or  either  one  of  these  causes)  amounts  to 
an  augmentation  or  diminution  of  the  sets  of  isodapanes.  Such 
expansions  or  contractions  will  therefore  increase  the  number  oi 
points  at  which  isodapanes  intersect,  just  as  bringing  the  sets  oi  l 
isodapanes  nearer  together  without  altering  the  size  of  each  indi-j  ^" 
vidual  isodapane  will  increase  the  number  of  intersections.  It  is 
therefore  permissible  to  regard  locational  weight,  transportationj 
costs,  and  distance  of  the  units  of  production  from  one  another 
— to  regard  all  of  them  as  a  sort  of  similar  mode  of  influence 
which  is  uniform  in  its  effect. 


What  does  this  expansion  of  unaltered  sets  of  isodapanes 
mean  with  respect  to  the  formation  of  segments,  and  therefore 
with  respect  to  the  scale  of  agglomeration?  To  begin  with,  it 
clearly  does  not  mean  the  same  thing  as  an  alteration  of  the 
order  of  the  isodapanes  in  the  scale — an  alteration  which  results 
from  changes  in  the  function  of  economy.  The  expansion  of 
unaltered  sets  of  isodapanes  must  not  be  confused  with  an  alter- 
ation of  the  order  of  the  isodapanes  in  the  scale.  But,  as  in  the 
latter  case  a  further  extension  of  the  higher  isodapanes  means 
facilitating  some  agglomerations,  so  bringing  the  sets  nearer  to- 

FiG.  31  Fig.  32 

igether  will  have  the  same  effect;  because  such  an  approach  ob-  146 
!  viously  increases  the  segments  and  aids  in  piling  up  sufficiently 
'large  quantities  of  production  within  the  segments;   in  other 
words,  the  two  decisive  factors  are  influenced  favorably,  and 
it  will  cause  agglomeration  to  take  place  on  a  larger  ''scale." 
"This  will  be  evident  from  the  above  figures,  which  are  simplified 
by  showing  a  function  of  economy  with  only  two  stages  (öi  and 
a.).  The  distance  of  the  isodapanes  (that  is,  the  function  of 
economy)  is  precisely  the  same  in  Figures  31  and  32 ;  the  figures 
differ  only  in  the  distance  between  the  units  of  production.  In 
Figure  3 1  the  distance  between  the  units  is  greater  than  in  Fig- 
ure 32,  where  they  have  been  brought  nearer  together  by  one 
quarter.  In  Figure  3 1  there  may  be  agglomeration  only  toward 


Ö1,  and  even  this  only  on  the  assumption  that  two  individual  in- 
dustrial units  will  suffice  to  make  up  the  required  quantity  of 
production.  In  Figure  32,  however,  there  are  (due  to  the  smaller 
distances  of  the  units  of  production)  possibilities  for  agglomer- 
ation toward  a^  and  Ö2,  if  we  assume  that  the  total  quantity  of 
production  of  all  four  units  of  production  is  necessary  and  suf- 
ficient to  make  up  the  required  quantity  for  a..  Under  that  as- 
sumption the  agglomeration  will,  in  fact,  take  place  in  the  direc- 
tion of  the  higher  unit  a^,  since  the  distance  between  the  critical 
isodapane  and  the  midpoint  of  the  segment  (point  of  agglomera- 
tion) is  greater  for  02  than  for  ax.  To  sum  up:  bringing  the  sets 
of  isodapanes  nearer  together  affects  the  "scale"  of  agglom- 
eration. It  affects  the  scale  of  agglomeration  less  than  varying 
the  function  of  economy  affects  it;  for  if  I  draw  the  locational 
figures  a  given  distance  toward  one  another  all  isodapanes,  in- 
cluding those  of  lower  order,  come  nearer  together.  The  gross 
economy,  therefore,  increases  at  every  step  in  the  scale,  but  more 
rapidly  in  the  higher  order  than  in  the  lower  order.  If,  however, 
I  affect  only  the  rate  of  succession  in  the  scale — if,  in  other 
words,  I  let  the  isodapanes  of  higher  order  extend  farther,  then 
only  these  isodapanes  of  higher  order  within  the  different  sets  of 
isodapanes  approach  one  another  and  the  gross  economy  of  ag- 
147  glomeration  increases  only  with  respect  to  them.  The  scale  of 
agglomeration  will  therefore  be  much  more  immediately  affected. 
Later  it  will  be  our  task  to  formulate  more  precisely  the  differ- 
ence in  the  measure  of  effectiveness  of  the  various  factors.  In  the 
meantime  this  indication  of  their  different  ways  of  working  must 

We  now  come  to  consider  the  second  part  of  the  third  fac- 
tor :  the  quantity  of  production  of  the  units  of  production.  We 
can  only  say  of  this  that  an  increase  of  it  quite  obviously  facili- 
tates agglomeration,  increases  its  "scale";  while  a  decrease  di- 
minishes it.  For  if  the  quantity  of  production  in  the  individual 
industries  increases  sufficiently,  the  common  segments  of  less 


widely  extended  isodapanes  will  now  contain  the  quantity  of 
production  requisite  for  a  unit  of  agglomeration.  Similarly,  sets 
of  isodapanes  which  formerly  did  not  have  the  requisite  quanti- 
ties in  common  segments  of  their  higher  isodapanes  will  now 
possess  them.  The  unit  of  production  may  even  "by  itself"  gain 
so  much  weight  that  it  represents  various  degrees  of  the  function 
of  economy  even  without  concentration;  and  one  may  imagine 
the  extreme  case  in  which  a  whole  function  of  economy  is  real- 
ized through  increasing  the  quantities  of  production  of  the  unit 
of  production  without  the  industry  necessarily  being  deviated. 
This  may  suffice  to  indicate  the  basic  effects  of  the  quantity  of 
production  upon  agglomeration.  It  is  impossible  to  give  more 
than  this  elementary  idea  here;  for  the  locational  figures  and 
their  isodapanes  fail  us  as  graphic  aids  in  clarifying  issues  in- 
volving the  quantities  of  production  of  the  units  of  production. 


It  is,  however,  possible  to  get  farther  by  other  means  in 
our  attempt  to  explain  the  significance  of  all  the  factors  taken 
together.  It  is  possible  to  arrive  analytically  at  a  precise  formu- 
lation of  the  degree  of  influence  of  the  various  factors  by  assum- 
ing that  industries  are  distributed  evenly  and  produce  every- 
where the  same  commodity.  We  may  thus  get  for  the  entire 
industry  an  insight  into  the  orientation  which  results  from  every 
combination  of  the  factors.  This  is  accomplished  by  the  formu- 
la of  agglomeration  as  set  forth  in  the  Appendix.^  But  it  is  im-  148 
portant  to  keep  in  mind  the  assumption  of  uniform  density  of 
industry  throughout  a  given  area,  an  assumption  which  will  not 
be  vaHd  for  any  actual  industry  or  any  actual  country.  The  for- 
mula, so  far  as  it  gives  us  the  number  and  size  of  the  centers  of 
agglomeration  arising  from  any  combination  of  the  various  fac- 
tors, has,  therefore,  only  a  theoretical  value.  It  gives  only  a  gen- 
eral idea  (probably  rather  far  removed  from  reality)  with  which 

^  Cf .  p.  246  f.,  infra. — Editor. 


we  can  compare  the  reality  without  necessarily  expecting  to  rec- 
ognize in  the  reality  the  picture  set  up  by  the  formula.  The  for- 
mula is  in  this  respect  only  an  aid  to  understanding.  But  that  is 
only  one  aspect  of  it.  The  formula  is  no  doubt  more  important  in 
so  far  as  it  enables  us  to  ascertain  with  precision  the  effect  which 
changes  in  any  one  of  the  factors  of  agglomeration  will  have 
upon  the  agglomeration  as  a  whole.  And  this  service  our  formula 
does  render,  not  only  theoretically,  but  also  for  any  given  case. 
Because  no  matter  how  many  different  degrees  of  density  are  ac- 
tually to  be  found  for  a  given  industry  in  different  localities,  the 
factors  in  question  must  be  operative  in  each  of  these  localities i 
(and  consequently  in  the  whole  body  of  that  industry)  accord- 
ing to  the  same  relative  degree  of  influence  which  they  would 
have  in  an  industry  distributed  smoothly  and  evenly.  Such 
even  distribution  of  industry  merely  represents  one  of  the  vari- 
ous grades  of  density  of  the  real  body  of  industry. 

Let  us  attempt  to  clarify  the  result  which  has  been  attained 
in  the  Appendix  and  translate  its  formulas  into  non-technical  lan- 
guage. Up  to  this  time  we  have  dealt  only  with  the  absolute 
economies  which  could  be  attained  per  ton  of  product  in  each 
stage  of  agglomeration.  These  economies  were  treated  as  a  func- 
tion of  the  size  of  the  agglomeration,  the  concept  "function  oi 
economy"  being  utilized.  One  may,  however,  according  to  the 
Appendix,  inquire  into  the  relative  increase  of  economies  which 
takes  place  as  there  is  an  increase  in  the  size  of  the  agglomera- 
tion, i.e.,  the  increase  of  economy  which,  starting  from  any  given 
stage  of  agglomeration,  is  attained  by  the  addition  of  anothei 
industrial  unit.  And  since  this  increase  of  economy  depends 
solely  upon  the  stage  of  agglomeration  already  reached — if  we! 
imagine  the  small  units  as  small  enough  in  comparison  to  the 
large  ones  which  attract  them — we  shall  recognize  a  second  func 
tion  which  expresses  the  power  of  attraction  of  the  various  stages 
of  agglomeration.  This  second  function  is  called  in  the  Appen 
149  dix  the  ''function  of  agglomeration."  The  function  of  agglom 


eration  f(M)  is  composed  of  the  additional  saving  which  cor- 
responds to  each  step  of  progress  from  one  stage  of  agglomera- 
tion to  another.  In  the  Appendix  the  relation  of  this  function  of 
agglomeration  to  the  function  of  economy  (with  which  we  have 
previously  dealt)  is  analyzed;  it  is  shown  that  the  two  functions 
are  intimately  connected,  and  it  is  shown  in  what  manner  they 
are  connected. 

All  that  concerns  us  at  the  present  time  is  the  fact  that  the 
function  of  agglomeration  expresses  with  precision  the  power  of 
attraction  which  a  large  unit  of  industry  exercises  over  scat- 
tered smaller  units.  As  the  equation  (Bestimmungsgleichung) 
for  the  extent  to  which  a  large  unit  attracts  smaller  units,  we  get 

the  formula  R=^  ~\'^  ^^  which  R  is  the  radius  of  agglomeration 

as  extended,  A  the  locational  weight  of  the  industry,  and  s  the 
transport  rate  which  prevails.  Thus  we  find  that  the  attraction 
of  a  large  unit  of  industry  is  directly  proportional  to  the  value  of 
the  function  of  agglomeration,  and  inversely  proportional  to  the 
locational  weight  of  the  industry  and  the  prevailing  transport 

So  much  for  the  relevance  of  these  three  factors  of  agglom- 
eration. If  we  wish  to  get  an  insight  into  the  actual  extension  of 
the  radii  of  agglomeration  and  to  determine  the  actual  amount 
of  agglomeration  it  is  necessary  to  take  into  account  the  thus- 
far  neglected  fourth  factor  of  agglomeration,  the  ''density  of  in- 
dustry." The  density  of  industry  ( p )  determines  the  length  of 
the  radius  (R)  which  is  necessary  in  order  to  bring  together  any 
given  quality  of  agglomeration  (M).  The  formula  is  as  follows: 

M  =  TrR'p, 



If  we  introduce  this  value  into  the  equation  of  agglomeration, 
instead  of  the  unknown  radius  of  agglomeration,  R,  we  get: 

M    AM) 


Trp        AS 

150  or 


V   TTp 

The  meaning  of  this  formula  may  be  interpreted  as  follows:  As- 
suming that  the  locational  weight  of  an  industry  {A),  the  rate 
level(5),  and  the  density  of  industry  (p)  are  known,  we  must  in- 
sert into  the  formula  that  value  of  (M),  i.e.,  that  magnitude  of 


agglomeration  with  which  some  value  of  /(ikf)=— 7=  V Mi  i^ 

V  TTp 

we  wish  to  know  which  of  the  possible  values  of  a  function  of  ag- 
glomeration j{M)  of  an  industry  will  become  effective,  or,  in 
other  words,  if  we  wish  to  know  what  ''scale"  of  agglomeration 
will  actually  become  a  factor  for  an  industry  when  the  conditions 
of  agglomeration  are  known.  This  formula  solves  the  problem. 
The  Appendix  shows  in  a  simple  manner  how  one  may  deter- 
mine by  diagram  whether  an  effective  M,  which  corresponds  to 
these  conditions,  exists  at  all,  and  therefore  whether  any  ag- 
glomeration will  take  place.  It  shows  also  how  we  can  deter- 
mine the  value  of  M.  The  Appendix  brings  out  further  that  if 
we  know  the  size  of  the  individual  units  of  agglomeration  we  also 
know  the  number  of  centers  of  agglomeration  which  will  arise  in 
any  area  with  a  known  total  production.  We  get  the  number  of 
centers  of  agglomeration  by  dividing  the  total  quantity  (G)  by 
the  value  of  the  single  agglomerations. 


What  has  been  considered  up  to  this  point  has  applications 
to  the  influence  of  the  forces  of  agglomeration  upon  industries 
oriented  at  the  points  of  minimum  costs  of  transportation.  What 



will  be  the  result  if  the  forces  of  agglomeration  are  considered 
for  industries  oriented  at  the  labor  locations  ? 

In  order  to  analyze  what  happens  in  this  case  we  shall  do 
well  to  bear  in  mind  that  labor  orientation  is  one  form  of  devia- 
tion from  the  minimum  point ;  agglomeration  is  another.  When 
agglomerative  forces  appear  in  an  industry  oriented  toward  la- 
bor, there  takes  place  a  competition  between  the  agglomerative 
deviation  and  the  labor  deviation,  a  struggle  to  create  "locations 
of  agglomeration,"*^  as  compared  with  "labor  locations,"  both  be- 
ing upon  the  foundations  of  the  transportational  groundwork.  151 
That  one  of  the  two  forces  which  can  offer  the  greater  net  econ- 
omies over  and  above  the  transport  orientation  will  be  the  victor. 

It  might  at  first  thought  be  held  that  if  we  are  to  consider 
pure  competition  between  agglom-locations  and  labor  locations 
we  should  simply  compare  the  net  economies  of  agglomeration 
with  the  net  economies  of  labor.  But  this  is  not  the  correct  plan 
of  attack,  for  a  labor  location  may,  and,  as  we  already  know,  in 
most  cases  will,  itself  be  a  point  of  agglomeration — accidental 
agglomeration,  we  have  called  it.  In  connection  with  this  acci- 
dental agglomeration  economies  of  agglomeration  will  occur,  and 
these  economies  will  be  precisely  in  accord  with  that  measure  of 
the  function  of  economy  which  the  agglomeration,  according  to 
its  size,  represents.  These  economies  of  agglomeration  are  sep- 
arate and  distinct  from  the  economies  of  labor  which  attract  in- 
dustry toward  that  particular  labor  location.  These  economies 
Df  accidental  agglomeration  must  therefore  be  added  to  the  econ- 
Dmies  of  labor  if  we  wish  to  know  the  total  amount  of  economies 
with  which  the  labor  locations  compete  with  the  purely  transpor- 
:tational  locations  of  agglomeration.  The  question  then  is.  Which 
is  larger,  the  economies  of  agglomeration  at  such  agglom-loca- 
tions, or  the  economies  of  labor  plus  the  economies  of  accidental 
agglomeration  at  the  labor  locations? 

^  Hereafter  occasionally  referred  to,  for  brevity's  sake,  as  "agglom-locations." 



That  means  that  all  industries  in  the  case  of  which  acciden- 
tal agglomeration  at  labor  locations  creates  units  of  agglomera- 
tion as  great  as,  or  greater  than,  pure  and  independent  agglom- 
eration within  the  groundwork  of  transport  orientation  retain 
their  labor  orientation.  For  in  such  a  case  the  economies  due  tc 
this  accidental  agglomeration  are  greater  than  those  which  the 
agglom-locations  can  offer.  Only  those  industries  in  the  case  o: 
which  the  accidental  agglomeration  creates  smaller  units  of  agi 
glomeration  can  possibly  be  otherwise  oriented.  But  this  wil 
happen  only  when  the  loss  of  economies  of  agglomeration  (re* 
suiting  from  the  smallness  of  the  unit)  is  not  compensated  foj 
by  the  economies  of  labor  which  are  offered  by  the  labor  lo^ 

It  is  necessary  to  keep  two  things  in  mind:  First,  Industrie« 
with  a  highly  developed  labor  orientation  have  a  selection  of  la 
bor  locations  due  to  the  competition  of  such  locations  with  oi 
another.  This  very  process  of  selection  causes  a  considerabl 
152  accidental  agglomeration  at  the  more  favorable  labor  locations; 
labor  orientation  itself  shows  a  tendency  to  agglomerate.  Seq 
ond,  the  strength  of  this  tendency  to  agglomerate  depends  upo 
three  of  the  four  factors  upon  which  the  strength  of  the  inde 
pendent  tendency  toward  agglomeration  depends.  Locations 
weight,  rates  of  transportation,  and  density  of  population  affec 
labor  orientation  and  its  accompanying  accidental  agglomeratio 
in  the  same  way  and  just  as  much  as  they  affect  the  competin 
independent  or  pure  agglomeration.  Consequently  the  fourti 
factor  must  differ  very  greatly  indeed  if  it  is  to  prevent  the  aco 
dental  agglomerations  due  to  labor  orientation  from  being  s 
large  that  (with  their  economies  of  labor  added)  they  do  nc 
overcome  the  independent  agglomerations.  Thus  only  Industrie 
which  have  a  very  high  function  of  economy  and  a  very  wea 
labor  orientation  (and  therefore  very  small  accidental  agglorr 
erations  at  the  labor  locations)  can  be  subject  to  a  successfi 
competition  by  pure  and  independent  agglomeration.  Indepenc 



ent  agglomeration  within  the  groundwork  of  transport  orienta- 
tion will  not  eliminate  possible  labor  orientation  in  any  large 
proportion  of  industry. 

On  the  contrary,  the  addition  of  economies  of  agglomeration 
to  labor  economies  will  in  important  sections  of  industry  (name- 
ly, in  all  cases  in  which  a  large  agglomeration  is  due  to  labor  ori- 
entation) strengthen  labor  orientation  as  compared  with  trans- 
port orientation.  For  wherever  the  accidental  agglomerations 
caused  by  the  labor  locations  are  larger  than  any  possible  inde- 
pendent agglomerations  within  the  groundwork  of  transport  ori- 
entation, the  balance  between  the  two  is  added  to  the  economies 
of  the  labor  location  as  an  economy  not  otherwise  to  be  attained, 
and  this  strengthens  the  power  of  attraction  of  the  labor  loca- 
tion. 153 

We  can  make  clear  the  significance  of  these  influences  by 
the  following  example,  chosen  quite  at  random:  Let  us  examine 
the  effect  of  the  following  function  of  economy  for  a  series  of 
different  industries: 

No.  of  tons     .      .    100       200       300      400       500       600       700       800 
per  ton.     .     .        i  4  6  7  7.5       7.75      7.82      7.88 

What  will  be  the  effect  of  these  economies  of  agglomeration 
in  industries  with  labor  costs  of  $10,  $50,  $100,  $200,  $300  per 
ton  of  product?  Let  us  suppose  that  the  labor  economies  at  the 
labor  locations  amount  everjrwhere  to  10  per  cent.  Let  us  sup- 
pose further  that  the  accidental  agglomerations  which  occur  in 
consequence  of  labor  orientation  amount  to  50,  100,  200,  400, 
800  tons.  The  unit  of  independent  agglomeration  within  the 
groundwork  of  transport  orientation  which  can  be  attained  in 
accordance  with  the  aforementioned  function  of  economy  is,  of 
course,  the  same  in  all  the  industries.  Let  us  say  it  is  300  tons. 

Then  Table  I  will  show  how  ''independent  agglomeration" 
and  ''labor  orientation"  compare  with  each  other  for  the  various 



We  find  three  groups  of  industries:  First,  there  are  indus- 
tries with  a  very  small  index  of  labor  costs  (of  less  than  $50  per 
ton  of  product,  Group  i )  in  which  labor  orientation  is  in  itself 
so  weak  that  it  can  only  cause  small  deviations  and  concentra- 
tions. In  this  case  we  find  a  superiority  of  the  independent  ag- 
glomeration with  its  larger  units  of  agglomeration  and  greater 
economies  (5:1);  such  a  state  of  affairs  leads  to  orientation  to- 
ward agglom-locations  within  the  groundwork  of  transport  ori- 
entation.  However,  such  a  type  of  change  in  location  cannot- 


A.  Labor  Orientation 

B.  Agglomeration 

C.  Extent 
to  Which 

Economies  op 
A  Exceed 

Those  of  B 

Labor  Cost 
perT.  P.* 

per  T.  P. 

Unit  of 
tion (tons) 

per  T.  P. 

Unit  of 
tion (tons) 

per  T.  P. 


Group  I 

Group  II. . . 

Group  III. . 














-   4 

+    I 
+  9 
+  22 
+32.8     i 

*T.  P.  =  ton  of  product.  i 


bring  with  it  any  considerable  movement,  since  industries  which 

are  subject  to  it  have  only  been  slightly  deviated  anyway.  Foi 

that  reason  the  movements  of  this  group  of  industries  cannot 

154  have  very  great  practical  significance. 

Second,  there  are  industries  in  which  the  units  of  independ 
ent  agglomeration  are  larger,  to  be  sure,  than  the  units  of  ag^j 
glomeration  due  to  labor  orientation  (300  as  compared  with  loc! 
and  200  tons.  Group  II).  But  the  addition  of  these  economies  of 
accidental  agglomeration  to  the  labor  economies  make  the  totaii 
economies  due  to  labor  orientation  larger  than  the  economies 
due  to  independent  agglomeration  within  the  groundwork  oi 
transport  orientation.  Consequently  the  orientation  toward  la- 
bor locations  takes  place.  (The  ratios  of  economies  are  6: 5  andi 


And  third,  there  are  industries  in  which  the  units  of  agglom- 
eration at  labor  locations  are  larger  than  those  of  the  independ- 
ent agglomeration  (400  and  800  as  compared  with  300),  and  in 
which  the  addition  of  the  economies  of  agglomeration  cannot 
but  strengthen  the  influence  of  the  labor  orientation.  But  grant- 
ed that  these  additional  economies  (due  to  accidental  agglom- 
eration at  the  labor  locations)  strengthen  labor  orientation  in 
general,  how  will  they  affect  these  industries  within  the  ground- 
.work  of  labor  orientation? 

I  In  general  we  may  say  that  they  will  lengthen  the  radius  of 
attraction  of  the  labor  locations  in  much  the  same  way  as  do  the 
additional  transport  economies  resulting  from  the  replacement 
of  material  deposits  (cf.  supra,  p.  113).  We  can  measure  the  at- 
tracting power  of  each  individual  labor  location  only  if  we  add 
to  the  labor  economies  which  it  offers,  not  only  those  economies 
resulting  from  the  replacement  of  deposits,  but  also  all  the  econ- 
omies of  accidental  agglomeration  which  result  from  the  total 
amount  of  production  attracted. 

This  will  mean,  for  the  final  orientation  of  the  industry, 
(irst,  that  particles  of  the  industry  which  would  otherwise  have 
remained  oriented  at  the  points  of  minimum  cost  of  transporta- 
tion will  be  deviated  to  the  labor  locations.  Due  to  the  addi- 
tional economies  of  accidental  agglomeration,  labor  orientation 
2S  a  whole  will  prevail  over  transport  orientation  where  it  would 
lot  otherwise  prevail.  And  it  will  mean,  second,  that  within  the 
labor  orientation  of  the  industries  the  strong  labor  locations 
(which  by  virtue  of  the  large  percentages  of  "cost  reduction" 
which  they  can  offer  have  already  attracted  the  weaker  ones  to 
hemselves)  get  a  further  ''advantage,"  because  the  amount  of 
Droduction  agglomerated  in  them  represents  units  of  agglomera- 
:ion  having  economies  of  agglomeration.  The  radius  of  their  at-  155 
Taction  will  consequently  be  further  extended,  and  they  will  at- 
:ract  the  production  of  weaker  locations  still  farther  away.  The 
strength  of  labor  orientation  itself  will  be  still  more  accentuated. 



The  essential  effect  which  the  tendencies  to  agglomeration 
will  have  on  labor  orientation  is  to  increase  its  inherent  tenden- 
cies toward  concentration  at  a  few  locations. 




If  we  now  attempt  to  fit  the  results  of  the  preceding  para- 
graphs into  the  actual  development  of  our  economic  system  we 
do  so  because  we  wish  to  make  the  meaning  of  these  results  a  bit 
more  clear.  But  we  are  not  concerned  with  an  inductive  verifica- 
tion of  these  results. 


For  this  purpose,  and  only  for  this  purpose,  we  undertake 
to  discuss  the  question:  upon  w^hat  qualities  of  a  particular  in- 
dustry does  the  amount  of  its  agglomeration  depend,  a  questioi 
which  we  had  eliminated  for  methodological  reasons.  This  ques 
tion  causes  us  to  examine  more  carefully  those  conditions  of  ag 
glomeration  which  depend  upon  the  nature  of  the  particula 

There  are  two  such  conditions:  the  locational  weight  anc 
the  function  of  economy.  Of  these,  the  locational  weight  is  i 
simple  and  obvious  characteristic  of  every  industry,  and  it  con 
tains  no  problem.  We  need  not  stop  to  discuss  it. 

But  the  function  of  economy  is  another  matter.  It  is  no 
something  visible  and  tangible,  but  something  quite  indefinite 
in  its  way  it  is  merely  the  product  of  certain  other,  more  deepb 
rooted  characteristics  of  each  industry.  We  cannot  know  by  de 
duction  upon  which  characteristics  of  a  given  industry  this  func 
tion  of  economy  depends,  and  we  cannot  know  by  deduction  hov 
it  depends  upon  them.  Nor  would  it  enable  us  to  determine  thesi 
characteristics  more  fully  if  we  could  render  more  explicit  thi 
mode  by  which  this  function  of  economy  has  been  created,  a; 



has  been  attempted  in  the  section  entitled  ''Agglomerative  Fac- 
tors." To  be  sure,  it  is  manifest  that  there  is  a  connection  be-  156 
tween  the  function  of  economy,  the  agglomerative  factors  by 
which  this  function  is  created,  and  the  character  of  the  different 
industries;  moreover,  it  is  manifest  that  the  two  most  essential 
groups  of  agglomerative  factors  (namely,  the  development  of 
the  labor  organization  and  the  development  of  the  technical  ap- 
paratus of  each  industry)  will  create  a  varying  function  of  econ- 
omy with  varying  units  of  agglomeration.  But  we  cannot  de- 
duce definite  rules  which  state  what  qualities  of  a  given  industry 
will  determine  the  size  of  the  units  of  agglomeration  and  their 
succession,  in  short,  the  shape  of  the  function  of  economy.^ 

If  we  would  secure  a  general  idea  of  the  function  of  econ- 
omy and  if  we  would  understand  its  relation  to  the  character  of 
industries  we  must  start  from  quite  another  consideration.  Only 
industries  with  products  whose  value  is  to  a  large  degree  a  result 
Df  the  industrial  (or  formative)  process  itself  can  possibly  have 
ilarge  units  of  agglomeration  with  resultant  high  percentages  of 
compressible^  costs — an  effective  function  of  economy.  We  may 
5ay  that  such  industries  show  a  high  "value  added  through  man- 
ifacture"  (Formwert) }°  The  reason  why  only  industries  with 
juch  a  high  value  added  through  manufacture  will  have  an  effec- 
;ive  function  of  economy  is  simple.  We  know  it  already  from  the 
malogous  reasoning  about  the  labor  value  and  the  index  of  labor 
:ost.^^  There  we  said  that  only  where  high  labor  costs  per  ton  of 
oroduct  exist  can  considerable  labor  economies  per  ton  of  prod- 
ict  be  effected;  and  the  same  consideration  holds  good  for  man- 

^  Cf .  here  the  Mathematical  Appendix,  below. — Editor. 

^  Cf.  supra,  p.  106, — Editor. 

"  The  meaning  of  this  term  Formivert  is  best  rendered  by  "value  added  by 
Qanufacture."  But  since  manufacturing  is  the  process  of  giving  "form"  to  coarse 
Qaterials,  "form-value"  may  not  be  an  impossible  term.  A.  Predöhl  uses  it.  Cf. 
'ournal  of  Political  Economy,  XXXVI,  371  ff.  Moreover,  there  is  the  already 
stablished  term  form-utility. — Editor. 

"  Cf.  supra,  p.  107. 


ufacturing  costs  in  general,  including  the  costs  of  machinery,  etc. 
These  manufacturing  costs,  speaking  generally,  appear  in  the 
value  added  through  manufacture  of  a  product.  They  can  show 
high  indices  of  economy  through  high  percentages  of  compressi- 
bility, only  provided  the  costs  themselves  are  high.  These  gener- 
al manufacturing  costs  are  the  very  ones  which  the  effective  elab- 
oration of  the  working  force  and  of  the  technical  apparatus  (the 
two  most  important  groups  of  agglomerative  factors)  tend  to  re- 
duce. They  represent  the  most  essential  object  of  cost  reduction 
through  agglomeration.  But  even  the  elaboration  of  the  working 
force  and  of  the  technical  apparatus  creates,  first,  large  units  of 
agglomeration,  and  second,  high  percentages  of  compression  of 
the  large  units  as  compared  with  the  small  units ;  these  two  devel- 
opments will  be  of  moment  for  the  orientation  of  an  industry 
only  provided  the  value  added  through  manufacture  of  that  in- 
dustry per  ton  of  its  product  is  high.  We  shall  call  this  value  add- 
ed through  manufacture  per  ton  of  product  the  index  of  value 
added  through  manufacture  of  that  particular  industry  or  simplj 
157  index  of  manufacture.  If  that  index  rises,  equal  percentages  o} 
cost  reduction  of  equal  units  represent  greater  economies  per  tor 
of  product,  and  the  corresponding  critical  isodapanes  of  the  loca- 
tional  figures  will  be  farther  extended,  the  attracting  force  of  tht 
unit  of  agglomeration  will  increase,  etc. 

To  the  extent  to  which  this  index  of  value  added  througl 
manufacture  is  the  object  of  all  attempts  to  reduce  cost  througl: 
agglomeration — and  we  have  noted  that  the  two  most  importanii 
groups  of  agglomerative  factors  work  in  that  way — this  indej 
affords  us  a  rod  for  measuring  the  effective  tendency  toward  ag-; 
glomeration  of  industries.  It  must  be  said,  however,  that  this 
measuring  rod  does  not  tell  us  anything  final  concerning  the  ac 
tual  trend  toward  agglomeration  of  a  particular  industry,  and  ii 
does  not  tell  us  its  actual  function  of  economy;  it  only  outlines 
the  effective  tendency  toward  agglomeration.  For  this  measur- 
ing rod  does  not  point  out  which  reductions  exist  in  reality  (duti  j. 


to  the  elaboration  of  the  working  force  and  of  technical  appa- 
ratus) ,  nor  does  it  tell  what  is  the  order  of  succession  of  the  units 
of  agglomeration.  But  since  we  do  not  have  clear  knowledge 
concerning  the  dependence  of  the  function  of  economy  and  of 
the  virtual  agglomeration  of  industries  upon  the  general  charac- 
ter of  these  industries,  we  may  just  as  well  use  the  measuring 
rod  which  is  at  hand.  This  being  true,  we  shall  do  well  to  ex- 
amine this  index  of  value  added  through  manufacture  a  bit  more 
carefully,  and  to  relate  it  to  the  second  general  characteristic  of 
the  industries,  their  locational  weight. 

The  value  added  through  manufacture  of  an  industry  has  two 
main  constituent  factors:  the  labor  costs  expressed  in  wages 
and  salaries,  and  the  costs  of  machinery,  the  latter  to  be  inter- 
preted in  their  widest  sense,  as  including  interest  and  amortiza- 
tion of  fixed  capital  and  cost  of  power.  We  shall  distinguish 
these  two  as  "value  added  through  labor"  and  ''value  added 
through  machines."  Now  it  is  of  the  greatest  importance  (if  we 
are  to  use  the  index  of  manufacture  as  a  measuring  rod  of  ag- 
glomeration) to  know  in  what  proportion  those  two  factors  enter 
into  that  index.  To  the  extent  to  which  the  value  added  through 
manufacture  results  from  machines,  a  factor  curbing  agglomera- 
tion appears.  This  factor  is  the  increasing  use  of  fuel,  which 
means  a  rising  material  index  of  the  particular  industry.  We  can  158 
say  that  value  added  through  labor  is  a  pure  factor  of  agglomer- 
ation, while  the  factor  of  value  added  through  machines  is  to  a 
large  extent  paralyzed  by  a  rising  material  index.  This  fact  does 
not  prevent  us  from  using  the  value  added  through  manufacture 
of  an  industry  as  a  virtual  measuring  rod  of  its  agglomeration,  if 
only  we  do  not  forget  to  take  into  equal  consideration  the  second 
measuring  rod  which  is  contained  in  the  material  index  and  the 
locational  weight.  This  necessity  of  keeping  both  rods  in  mind 
suggests  that  we  relate  the  notion  of  the  value  added  through 
manufacture  to  that  of  the  locational  weight  and  create  a  con- 
necting concept  out  of  the  index  of  manufacture  and  of  the  loca- 


tional  weight,  just  as  we  have  previously  done  in  the  case  of  the 
index  of  labor  costs  and  of  locational  weight  for  our  analysis  of 
labor  orientation/-  This  is  possible  by  relating  the  index  of  man- 
ufacture, not  to  the  ton  of  product,  but  to  the  total  weight  which 
has  to  be  transported — the  ' 'locational  ton."  In  analogy  to  the 
term  "labor  coefficient"  used  earlier,  we  shall  suggest  the  term 
''coefficient  of  manufacture"  in  order  to  describe  the  value  added 
through  manufacture  per  locational  ton.  Now  we  can  formulate: 
industries  with  high  coefficient  of  manufacture  show  strong  tend-  i 
encies  to  agglomerate;  industries  with  low  coefficient  of  manu- 
facture show  weak  tendencies  to  agglomerate ;  and  these  tend- 
encies are  inherent  in  their  nature.  This  formula  is  comparative- 
ly simple,  but  it  must  be  remembered  that  a  considerable  number 
of  assumptions  have  been  made  in  the  process  of  constructing  it. 


Let  us  ask  next  what  will  be  the  practical  consequences  oi 
this  agglomeration  whose  general  rules  we  have  just  outlined  anc* 
whose  underlying  forces  we  have  characterized  in  detail.  Ir 
what  forms  shall  we  find  it  in  reality? 

It  will  be  remembered  that  agglomeration  may  influence 
both  transport-oriented  industries  and  labor-oriented  industries 
It  influences  labor-oriented  industries  simply  by  increasing  theii 
contraction  of  labor  locations  (according  to  rules  we  have  al 
ready  discussed) .  Only  industries  with  a  very  weak  tendency  tc 
labor  orientation  show  pure  and  independent  orientation  withir 
J  (-Q  the  groundwork  of  transport  orientation  instead  of  showing  la« 
bor  orientation. 

It  will  also  be  remembered  that  considerable  technical  ag 
glomeration  occurs  only  in  connection  with  a  high  coefficient  o: 
manufacture,  and  this  coefficient  is  composed  of  value  addec 
through  labor  and  through  machines.   But  since  value  addec 

^  Cf.  supra,  p.  no. — Editor. 




through  machines  is  always  connected  with  considerable  con- 
sumption of  material  (coal),  such  value  can  hardly  cause  the  co- 
efficient to  be  a  high  one  on  account  of  the  resulting  high  loca- 
tional  weight,  unless  a  considerable  increase  in  the  consumption 
of  human  labor  (value  added  through  labor)  occurs  at  the  same 
time.  Consequently  industries  with  a  high  coefficient  of  labor  will 
show  the  strongest  tendencies  of  agglomeration — as  long  and  in 
so  far  as  machines  mean  considerable  consumption  of  material. 
But  these  industries  are  strongly  labor-oriented  and  therefore 
already  agglomerated. 

The  main  consequence  of  technical  agglomeration  will,  un- 
der present  conditions,  be  found  to  be  a  strengthening  of  labor 
orientation.  The  other  consequence,  that  of  altering  the  trans- 
port orientation  by  creating  independent  agglomerations,  is  in- 
significant in  comparison.  For  in  the  case  of  this  latter  conse- 
quence the  agglomerating  tendency  operates  generally  with  a 
low  coefficient  of  manufacture,  and  is  therefore  itself  not  as 
strong  as  in  labor-oriented  industries. 

Two  results  follow  which  are  important  for  our  examination 
of  reality  later  on: 

First,  we  shall  find  the  transport-oriented  industries  some- 
what concentrated,  and  concentrated  not  very  far  away  from 
their  points  of  smallest  costs  of  transportation. 

Second,  wherever  we  encounter  an  industry  which  deviates 
considerably  from  its  transport  orientation  we  shall  be  safe  in 
assuming,  in  case  of  doubt,  that  it  is  an  industry  oriented  toward 
labor.  These  results  will  considerably  facilitate  our  later  analy- 
sis of  the  facts,  for  they  enable  us  to  separate  industries  into  two 
great  groups:  transport-oriented  and  labor-oriented  industries. 
This  makes  it  possible  for  us  to  approach  reality,  bearing  in 
mind  the  simple  issue  upon  which  this  distinction  is  based,  and 
to  neglect  (at  least  in  preliminary  studies)  all  more  detailed  dis- 
tinctions. 160 



Which  tendencies  of  development  shall  we  find  upon  closer 
examination  to  operate  upon  agglomeration  in  actual  life?  We 
know  the  different  conditions  of  agglomeration  from  our  analy- 
sis ;  they  are  density  of  population,  rates  of  transportation,  and 
coefficient  of  manufacture. 

The  tendencies  and  the  significance  of  the  first  two  condi- 
tions are  clear.  It  is  obvious  that  rising  density  of  population 
and  declining  costs  of  transportation  are  evolutionary  trends  of 
modem  times.  They  of  necessity  continuously  increase  agglom- 
eration. The  critical  isodapanes  of  the  locational  figures  are  in- 
cessantly extended  by  declining  costs  of  transportation,  and  this 
creates  effective  segments  of  higher  units  of  agglomeration; 
quantities  of  production  sufficient  for  higher  units  of  agglom- 
eration are  incessantly  created  by  the  increasing  density  of  the 
population,  and  this  at  the  same  time  pushes  the  locational  fig- 
ures closer  together.  It  is  hardly  necessary,  therefore,  to  take 
more  time  and  space  for  the  discussion  of  these  tendencies  of  de- 

But  the  significance  of  a  change  in  the  conditions  which  are 
deeply  rooted  in  the  general  character  of  a  given  industry  is  not 
quite  as  obvious.  Such  deep-rooted  conditions  are  implied  by  the 
coefficient  of  manufacture,  which  contains  value  added  through 
manufacture  and  locational  weight.  These  conditions  also  lead 
in  the  direction  of  agglomeration,  but  not  without  certain  curbing 
influences  becoming  effective. 

On  the  one  hand  the  value  added  through  manufacture  be- 
comes a  cause  of  considerable  agglomeration.  For  the  elabora- 
tion of  the  working  force  and  of  technical  apparatus  during  the 
eighteenth  and  nineteenth  centuries  meant,  as  is  well  known, 
the  creation  of  increasingly  large  frameworks  of  industrial  pro- 
duction. It  meant,  consequently,  the  creation  of  higher  units 
of  agglomeration  and  of  more  extensive  reductions  (compres- 
sions) of  the  index  of  manufacture  of  various  industries  in  cases 


in  which  these  higher  units  of  agglomeration  become  effective. 
To  express  these  observations  in  the  terms  of  our  theory,  this  de- 
velopment of  organization  and  technique  has  given  to  the  value 
added  through  manufacture  of  the  various  industries  that  signif- 
icance which  it  was  necessary  for  it  to  have  if  it  was  to  be  utilized 
in  the  creation  of  those  high  and  effective  units  of  agglomeration 
under  whose  influence  these  industries  have  been  ever  since.  In 
this  way  the  development  of  organization  and  technique  has 
doubtless  had  an  enormous  agglomerative  effect.  161 

On  the  other  hand  this  development  has  caused  forces  to  ap- 
pear which  curb  these  agglomerative  tendencies.  It  has  done  so 
by  its  influence  upon  the  consumption  of  materials,  which  con- 
sumption in  turn  influences  the  locational  weight.  The  creation 
of  those  new  big  frameworks  of  industrial  production  has  meant 
to  a  large  extent  the  replacement  of  manual  labor  by  mechanical 
apparatus,  and  it  has  meant  the  replacement  of  value  added 
through  labor  by  value  added  through  machines.  In  consequence 
of  all  this  the  weights  which  must  be  moved  for  production  are 
increased,  the  isodapanes  around  the  locational  figures  are  con- 
tracted, and  there  is  an  increase  of  the  resistance  which  the  high 
units  of  agglomeration  have  to  overcome  in  order  to  come  into 
existence  at  all. 

The  tendencies  of  modern  development  have,  on  the  one 
hand,  given  to  the  coefficient  of  manufacture  a  considerably  in- 
creased significance  so  far  as  agglomeration  is  concerned;  but 
they  have,  on  the  other  hand,  reduced  the  revolutionary  effect  of 
these  new  units  of  agglomeration  by  reducing  this  same  coeffi- 
cient of  manufacture  (due  to  a  process  of  "materiahzation"  of 

We  must  keep  all  these  facts  in  mind  if  we  would  understand 
the  part  played  by  agglomerating  tendencies  in  the  industrial 
revolution  of  the  eighteenth  and  nineteenth  centuries.  It  is  ob- 
vious from  the  viewpoint  of  this  part  of  our  theory  that  the 
change  from  handicraft  to  factory  production  (which  consti- 


tutes  the  most  important  aspect  of  this  revolution)  is  a  gigantic 
process  of  agglomeration.  Previous  to  this  development  even 
those  parts  of  production  which  (due  to  high  coefficients  of  manu- 
facture) were  in  themselves  capable  of  considerable  agglomera- 
tion had  remained  distributed  in  individual  producing  units, 
which  were  mostly  situated  at  the  places  of  consumption,  be- 
cause of  the  low  prevailing  material  index,  as  has  been  pointed 
162  out.  For  all  these  industries  the  discovery  of  the  fact  that  their 
index  of  manufacture  was  capable  of  great  reductions  within 
new,  highly  developed  frameworks  of  production  meant  their 
gradual  readjustment — the  revolution  before  referred  to.  This 
revolution  does  not  appear  in  its  full  severity  until  the  rapid 
rise  of  population  is  accompanied  by  an  equally  rapid  decline 
of  the  transportation  rates  during  the  nineteenth  century.  But 
what  will  take  the  place  of  the  old  crafts,  how  far  agglomera- 
tion will  extend,  what  magnitude  of  agglomerative  units  will  be 
developed,  at  what  points  the  centers  of  agglomeration  will  be 
fixed — all  these  matters  depend  quite  considerably  upon  how  the 
material  index  of  industries  is  changed  by  the  development  of 
technique  and  organization  in  these  industries.  In  other  words, 
these  matters  depend  upon  to  what  extent  their  locational  weight 
increases  and  their  coefficient  of  manufacture  decreases ;  to  what 
extent  the  coal  deposits  enter  in ;  and  how  far  the  otherwise  pre- 
vailing agglomeration  at  the  most  advantageous  labor  locations 
will  thus  be  interfered  with  by  an  agglomeration  resting  upon  | 
transport  orientation.  All  these  problems  appear  in  reality  as  a 
competition  of  the  labor  locations  with  the  coal  deposits.  The 
outcome  is  a  selection  of  the  labor  locations,  with,  however,  some 
attention  to  their  proximity  to  coal  deposits.  But  the  inductive 
part^^  will  show  that  we  have  usually  overestimated  the  extent 
to  which  agglomeration  at  the  coal  deposits  was  necessary;  by 

"Not  published.  Cf.  instead  Alfred  Weber's  contribution  to  the  Grundriss 
der  Sozialökonomik,  Vol.  VI,  "Industrielle  Standortslehre  (Allgemeine  und  kapi- 
talistische Theorie  des  Standortes)." — Editor. 


far  the  more  important  part  of  the  effectiveness  of  modern  ag- 
glomerative  units  was  the  increased  concentration  of  industries 
at  the  labor  locations,  and  this  was  coming  anyway.  It  will  also 
show  that  the  concentration  of  industries  at  the  coal  deposits 
represents  to  a  large  extent  a  reorientation  of  industries  which 
had  already  been  oriented  toward  material  deposits;  it  is  true 
that  they  were  different  and  more  widely  distributed  deposits. 
All  this  agglomeration  is  accidental  from  the  point  of  our  theory; 
it  is  not  technically  necessary.  Still,  we  shall  find  to  how  large 
an  extent  the  new  agglomeration  at  favorable  labor  locations  has 
been  influenced  by  the  increased  emphasis  upon  the  material 
aspect  of  production,  and  how  this  fact  has  influenced,  not  only 
the  emergence  of  the  attracting  labor  locations,  but  also  the  ex- 
tent of  agglomeration  at  these  labor  locations.  It  will  become 
apparent  in  this  connection  that  only  those  industries  have 
reached  the  highest  stages  of  ''technical"  agglomeration  in  which 
the  change  of  the  proportion  between  value  added  through  ma- 
chines and  value  added  through  labor  does  not  exceed  a  certain 
maximum.  163 

But  particularly  will  this  inductive  treatment"  show  that 
the  problem  of  agglomeration  is  not  exhausted  by  treating  that 
accidental  agglomeration  at  extensive  material  deposits,  partic- 
ularly coal  deposits,  and  not  even  by  treating  that  technically 
necessary  agglomeration  at  labor  locations ;  there  exist  over  and 
above  these  considerations,  and  exceeding  them  by  far,  kinds  of 
''social  agglomeration."  This  type  of  agglomeration  develops  at 
the  labor  locations  (largely  without  any  technical  necessity) 
•  upon  the  foundation  of  certain  rules  of  agglomeration  of  human 
labor.  It  will  be  one  of  the  main  tasks  of  the  inductive  treat- 
ment just  referred  to  to  show,  first,  in  which  particular  way  this 
social  agglomeration  with  its  creation  of  industrial  and  metro- 
politan districts  develops  on  top  of  the  simpler  and  more  limited 

"  Cf .  the  last  footnote. — Editor. 


forms  of  agglomeration  which  we  have  analyzed  in  the  forego- 
ing paragraphs.  We  shall  need  to  show,  second,  that  this  type  of 
agglomeration  does  not  evolve  from  causes  which  belong  to  a 
system  of  "pure"  economics  (which  we  have  discussed  previ- 
ously) but  that  it  is  the  consequence  of  quite  different  factors 
which  are  rooted  in  the  particular  social  structure  of  the  modern 
economic  system.  This  type  of  agglomeration  may  disappear  if 
164  the  social  structure  to  which  it  belongs  disappears. ^^ 

^^  This  point  is  more  or  less  well  brought  out  by  a  number  of  monographs 
published  since  Alfred  Weber's  theory  appeared.  Cf.  the  series  of  studies  edited 
by  himself,  Alfred  Weber,  Ueber  den  Standort  der  Industrien  II.  Teil:  Die 
deutsche  Industrie  seit  i860  beginning  with  Otto  Schlier,  "Der  deutsche  Industrie- 
körper seit  i860"  (1922).  For  an  analysis  of  recent  changes  Edgar  Salin,  "Stan- 
dortsverschiebungen der  deutschen  Volkswirtschaft"  (in:  Strukturwandlungen 
der  deutschen  Volkswirtschaft  [1928]  edited  by  Bernhard  Harms)  should  be  con- 
sulted. Particularly  interesting  to  the  American  student  are  two  recent  mono- 
graphs by  Andreas  Predöhl  in  the  Weltwirtschaftliches  Archiv,  "Die  Standorte 
der  amerikanischen  Eisen-  und  Stahlindustrie"  (1928)  and  "Die  Südwanderung 
der  amerikanischen  Baumwollindustrie"  (1929).  Finally  attention  may  be  called 
to  Hans  Ritschl,  "Reine  und  historische  Dynamik  des  Standorts  der  Erzeugungs- 
zweige" in  Schmollers  Jahrbuch  (1927),  and  Joh.  J.  Haurath,  "Zum  Problem  der 
hypothetischen  und  konkreten  Standortsbedingungen.  Dargelegt  am  Beispiel  dei 
Grosschlachterei  in  den  Niederlanden,"  in  Weltwirtschaftliches  Archiv  (1926).— 



We  have  so  far  built  up  our  theory  on  the  assumption  that 
the  activity  connected  with  the  productive  and  distributive  proc- 
ess of  an  industry  is  a  uniform  and  indivisible  thing  which  can 
only  as  a  whole  be  drawn  to  and  from  the  material  deposits  and 
the  place  of  consumption  by  locational  forces,  and  which  goes 
on  entirely  independent  of  the  activities  of  other  industries.  But 
this  indivisibility  of  the  productive  process  and  its  independence 
of  the  productive  processes  of  other  industries  do  not  in  fact 

We  must  now  take  the  following  facts  into  account:  First, 
the  productive  process  of  almost  every  industry  consists  of 
diverse  parts,  which  are  technically  independent  of  one  another 
and  can,  therefore,  be  undertaken  at  different  places.  We  may 
well  think  of  the  productive  process  as  a  heap  of  little  balls  which 
have  been  rolled  together  at  one  place  by  the  (dynamics  of  the) 
-ocational  factors  we  have  discussed,  but  which  may  be  redis- 
:ributed  by  those  factors.  Second,  the  forces  which  move  those 
ittle  balls  (those  parts  of  the  productive  process)  are  not  con- 
iined  within  a  particular  productive  process ;  rather  they  are  as- 
Dects  of  a  complex  of  larger  forces  resulting  from  the  intertwin- 
ng  of  the  different  parts  of  industrial  production  of  a  country. 
Ve  shall  designate  the  first  set  of  facts  as  the  organization  of  the 
tages  of  a  given  productive  process  or  enterprise  (Produktions- 
tuf engliederung),  and  the  second  set  as  the  interlacing  (Inein- 
nder greif  en)  of  the  independent  productive  processes.  165 








Let  us  suppose  that  an  industry  is  influenced  only  by  cost  of 
transportation,  and  let  us  neglect  all  the  deviating  influence  of 
labor  and  agglomeration.  What,  given  such  assumptions,  does  it 
mean  that  the  productive  process  does  not  need  to  be  entirely 
performed  at  one  location,  but  may  be  split  into  a  number  of 
parts  which  may  be  completed  at  different  locations? 

The  only  cause  which  could  lead  to  an  actual  split  and  to  a 
resultant  transfer  of  the  parts  to  different  locations  would  ob- 
viously be  that  some  ton-miles  would  be  saved  in  the  process. 
For  the  reduction  of  these  ton-miles  to  a  minimum  is  the  sole 
principle  regulating  transport  orientation — the  principle  which 
produces  the  locations  we  have  previously  discussed.  We  must 
accordingly  consider  whether  the  ton-miles^  are  lowered  if  the 
locations  of  the  stages  or  parts  of  production  are  separated.  li 
we  find  that  they  are  lowered,  we  shall  need  to  determine  where 
the  transport  locations  of  the  split  industry  will  be  situated. 

Let  us  take  a  simple  case,  an  enterprise  with  three  materia 
deposits  and  one  which  is  capable  of  being  split,  technologicall} 
speaking,  into  two  stages.  In  the  first  stage  two  materials  arc 
combined  into  a  half -finished  product  {Halbfabrikat) ;  in  thi 
second  stage  this  half-finished  product  is  combined  with  tht 
1 66  third  material  into  the  final  product.  Figure  33  shows  where  the 
location  P  of  the  unspHt  production  would  be  situated  according 
to  our  earlier  locational  rules,  assuming  certain  proportions  oi 
the  weight  of  materials  outside  and  inside  the  final  product.  Lei. 

^  We  shall  have  to  imagine  these  ton-miles  as  permeating  the  entire  produc-i 
tive  process,  of  course.  ' 



us  suppose  that  possible  locations  of  the  split  production  would 
be  in  Pi  and  P2 ;  Pi  for  the  first  stage  and  P2  for  the  second  stage. 
What  will  be  the  result  if  the  splitting  occurs?  Obviously,  we 
shall  have  two  locational  figures  with  three  roots  instead  of  one 
figure  with  four  roots.  The  first  locational  figure  is  M1M2P2; 
it  is  rooted  in  the  two  material  deposits  of  the  first  stage  of  pro- 
duction and  the  place  of  production  of  the  second  stage  of  pro- 
duction which  is  also,  obviously  enough,  the  place  of  consump- 
tion of  the  first  stage.  The  second  locational  figure  is  M^PiC; 

Fig.  33 

it  is  rooted  in  the  place  of  production  of  the  first  stage,  and  in  the 
location  of  the  additional  material  deposits,  and  in  the  place  of 
consumption  of  the  final  product.  Pi,  the  location  of  the  first 
stage  of  production  is  the  point  of  minimum  costs  of  transporta- 
tion,^ or  the  minimum  point,  as  we  have  called  it,  of  the  first 
locational  figure.  P2,  the  location  of  the  second  stage,  is  the 
ninimum  point  of  the  second  figure.  Thus  the  problem  of  the 
Vhere"  of  the  locations  of  stages  of  production  appears  to  be 
3ne  which  falls  within  the  realm  of  our  analysis.  It  involves  de- 
ermining  the  locations  of  the  corner-points  of  new  locational 
igures.  These  corner  points  are  the  locations  of  the  various 
;tages  of  production.  If  we  succeed  in  finding  these  comer- 
joints,  our  problem  is  solved,  since  these  corner-points  are  the 
ocations  of  split  processes  of  production.   The  mathematical 

^  Cf .  supra,  p.  53. — Editor. 


problem  involved  is  solved  in  Appendix  I,  §§8-ii/^  We  shall 
make  use  of  that  solution  at  this  point.  But  let  us  first  see  whether 
167  we  can  learn  from  the  foregoing  when  this  split  will  occur. 

To  attack  this  problem  we  must  alter  our  question.  The 
problem  is  not,  when  does  such  a  split  occur?  but  when  does  it 
not  occur?  When  does  production  remain  at  a  single  location? 
If  we  look  at  our  figures  again,  we  shall  see  at  once  that  the  oc- 
currence of  a  single  location  is  a  particular  case  among  the  many 
possible  locations  of  the  separable  stages  of  the  process  of  pro- 
duction. This  case  is  reaHzed  when  in  the  locational  figure  of  the 
first  stage  the  place  of  production  coincides  with  the  place  of 
consumption;  and  when  in  the  locational  figure  of  the  second 
stage  the  place  of  production  coincides  with  the  place  of  pro- 
duction (the  deposit)  of  the  unfinished  product  made  in  the  first 
stage.  If  such  coincidence  occurs,  the  two  locations  coincide.  In 
all  other  cases  they  lie  apart.  The  problem  as  to  when  a  split  of 
the  location  will  occur  resolves  itself  into  the  following  ques- 
tion :  Under  what  particular  condition  does  this  coincidence  of 
the  sites  of  the  separate  stages  of  production  occur?  We  may 
consider  this  question  first  with  reference  to  an  enterprise  which 
can  be  split  into  two  stages  only. 

One  is  inclined  at  first  blush  to  suggest  that  this  coinci- 
dence can  occur  only  in  case  the  site  of  the  first  stage  of  produc- 
tion is  located  (because  of  the  proportions  of  its  weights)  at  the 
place  of  consumption,  and  only  if,  furthermore,  the  place  of  pro- 
duction of  the  second  stage  is  (also  due  to  the  proportion  of  its 
weights)  situated  at  the  deposit  of  the  unfinished  product  of 
the  first  stage.  If  this  were  true,  the  non-occurrence  of  a  split 
would  be  a  very  rare  exception  (assuming  that  the  split  were  at 
all  possible  on  technical  grounds) ;  and  practically  all  productive 
processes  having  several  technical  stages  would  have  different 
locations  for  these  stages.  But  not  quite  so  many  conditions 
need  to  be  fulfilled.  It  is  sufficient  either  that  the  production  of 

^  Cf.  injra,  p.  234. — Editor. 


''■'  the  first  stage  is  located  at  the  place  of  consumption  or  that  the 
production  of  the  second  stage  is  located  at  the  deposit  of  the  un- 
finished product.  For  if,  upon  the  one  hand,  the  production  of 

■  the  first  stage  is  located  at  the  place  of  consumption,  then  it  will 

■  follow  any  location  of  the  second  stage  which  is  determined  by 
the  proportions  of  weight  within  the  second  locational  figure. 
It  will,  for  example,  go  to  the  place  of  consumption  of  the  sec- 

:  ond  stage,  or  to  one  of  the  material  deposits  or  to  any  interme- 
diate position.  The  fact  that  it  will  thus  follow  of  course  makes  168 
the  two  locations  coincident.  And  if,  upon  the  other  hand,  the 
'i  .location  of  the  second  stage  is  situated  at  the  deposit  of  the  un- 
5  finished  product,  the  location  of  the  second  stage  will  follow  the 
-location  of  the  unfinished  product  anywhere.  It  will,  for  exam- 
ple, go  to  the  original  material  deposits  or  to  any  intermediate 
position.  In  this  case  also  the  two  locations  are  of  course  coinci- 

It  is  accordingly  only  necessary  that  the  conditions  (weight 
proportions)  either  in  the  first  or  in  the  second  stage  be  such 
that  the  location  is  bound  to  follow  the  location  of  the  other 
stage,  and  the  split  will  not  take  place.  The  following  considera- 
tion will  indicate,  however,  how  frequently  this  split  will  take 
place,  provided  it  is  technically  feasible.  In  order  for  the  pro- 
duction of  the  second  stage  to  run  after  the  location  of  the  first, 
it  is  necessary  for  the  unfinished  product  to  enter  into  the  sec- 
ond stage  with  a  locational  weight  which  is  at  least  equal  to  the 
'■■  sum  of  the  weight  of  the  future  product  and  of  the  weights  of  the 
^'  added  materials — all  this  in  accordance  with  our  previous  rules. 
•  Jhis  means  that  the  product  will  have  to  lose  considerable  weight 
^  jduring  the  second  stage.  But  the  second  and  later  stages  of  indus- 
^  trial  productive  processes  are  usually  concerned  with  the  working 
up  of  pure  materials,  with  little  ehmination  of  waste  materials 
(Materialrückstände) .  These  stages  will  therefore  very  seldom 
'tave  such  a  location  unless  they  are  oriented  toward  coal  de- 
posits. So  much  for  that.  On  the  other  hand,  the  production  of 



the  first  stage  must  lie  at  the  place  of  consumption  if  it  is  to 
follow  the  production  of  the  second  stage.  This  means  that  there 
must  be  no  loss  of  material  during  the  first  stage,  or  at  least  only 
as  much  as  will  be  compensated  by  the  addition  of  ubiquities 
This  also  will  be  very  rare,  since  the  first  stage  of  industrial  pro- 
duction is  commonly  concerned  with  bringing  into  existence  the» 
pure  material,  a  process  which  calls  for  the  elimination  of  the 
waste  materials.  We  conclude,  then,  in  either  case  that  the  con- 
ditions leading  to  the  coinciding  of  the  two  locations  will  not  be 
frequent.  We  may  say,  even  on  the  basis  of  this  prehminary 
169  analysis:  Single  location  of  production  will  be  the  exception  and 
a  split  of  production  into  several  locations  will  be  the  rule  for 
productive  processes  which  can  technically  be  split. 


Our  next  question  is:  Where  will  the  locations  of  the  pro- 
ductive stages  be  when  production  is  split?  Our  answer  will 
make  it  possible  further  to  elaborate  upon  the  question  as  to 
when  such  splitting  will  occur. 

The  locations  of  the  stages  it  will  be  remembered,  can  be 
fixed  as  the  corner  points  of  the  new  locational  figures  in  which 
the  spHt  production  is  carried  on.  We  know  the  corresponding 
figures  which  have  to  be  constructed  within  these  locational  figi 
ures  according  to  the  general  locational  rules.  This  is  the  key 
by  which  the  unknown  corners  are  discovered,  as  is  shown  in 
Appendix  I,  §  11.^  These  unknown  corners  are  the  locations  oi 
the  stages  of  production.  I  refer  to  the  result  found  in  the  Ap^ 
pendix,  and  I  shall  here  apply  it  only  to  a  few  important  cases 

*The  reader  will  find  quite  tiring  the  reasoning  employed  in  this  and  thf 
following  parts  of  this  section.  It  is  really  not  intended  for  those  who  wish  tc 
get  the  general  trend  of  the  main  argument;  they  may  omit  it.  But  scientific 
precision  requires  that  this  analysis  be  undertaken ;  for  it  is  necessary  to  show  tc 
what  extent  the  mathematical  solutions  based  upon  our  theory  cover  the  mani- 
fold phenomena  and  problems  of  reahty. 

°  Cf.  p.  236,  infra. — Editor. 



Let  us  suppose  that  the  productive  process  spHts  into  stages 
-two  at  first,  each  of  which  combines  two  materials.  The  lo- 
^  cational  figures  for  these  stages  would  obviously  be  triangles. 
Since  we  know  the  weight  triangles  of  "the  two  locational  figures 
pi  with  one  unknown  corner,"  we  know  the  circles  upon  which  the 
I  two  unknown  corners,  the  two  locations,  will  lie.  (They  are  the 
i  two  circles  over  M1M2  and  M^C  of  the  following  figure.)  We 
ft  know,  further,  that  the  two  locations  will  lie  upon  one  straight 

Fig.  34 

Fig.  35 

line  (cf.  Appendix  I,  §§  9  and  11)  which  connects  two  easily  con- 
structed points  of  the  two  circles  (at  the  points  O  and  Oi  of  Fig- 
ure 34).  The  points  where  this  line  intersects  with  the  circles 
are  the  locations  of  the  split  production  (P  and  Pi  of  the  adjoin- 
ing figure).  It  will  be  seen  at  once  that  this  simple  rule  is  gen- 
erally applicable. 

Let  us  now  assume  a  productive  process  based  upon  two  ma- 
terials so  that  the  entire  process  will  be  carried  through  within 
one  locational  figure,  and  let  us  assume  that  it  is  possible  to 
split  the  process  so  that  the  first  stage  of  production  combines 
the  two  materials,  while  the  second  stage  uses  one  of  the  ma- 





terials  (for  example,  coal)  again  in  connection  with  the  unfin- 
ished product,  thus  completing  the  product.  The  diagram  which 
will  give  us  the  location  of  the  two  stages  is  simple  enough  (cf. 
foregoing  Figure  35).  The  circle  over  the  material  deposits  with 
the  angle  of  the  first  weight  triangle  as  its  peripheral  angle  will  be 
the  general  focus  of  the  first  location;  while  the  circle  with  the 
analogous  angle  of  the  second  weight  triangle  over  the  second 
material  deposit  and  the  place  of  consumption  will  be  the  general 
locus  of  the  second  location.  The  points  0  and  Oi  situated  upon 
the  circles  have  to  be  determined  next.^  The  two  points  at  which  1 

Fig.  36 

the  straight  line  connecting  them  intersects  the  circles  are  the- 
two  locations,  Pi  and  P2.  j 

Let  us  next  assume  a  productive  process  based  upon  five  ma- 
terials, it  being  a  process  which  might  technically  be  split  into 
three  stages.  The  first  stage  combines  the  first  two  materials; 
the  second  stage  combines  the  product  of  the  first  with  two  more 
materials;  and  finally  the  third  stage  combines  the  product  of 
the  second  stage  with  the  fifth  and  last  material  into  the  final 
171  product. 

The  diagram  showing  how  the  locations  of  these  stages  may 
be  determined  is  given  in  Figure  36. 

In  principle  the  diagram  of  the  case  when  the  production  is 
split  into  parallel  instead  of  successive  stages  is  quite  similar. 
Let  us  take  for  example  car  manufacturing.   Here  the  metal 

®  Cf.  Appendix,  p.  237,  infra. — Editor. 



parts  are  worked  up  into  unfinished  products  in  steel  foundries 
and  metal  works;  other  parts  are  worked  up  in  wood  manufac- 
turing processes;  and  still  others  are  worked  up  into  half-fin- 
ished products  in  sundry  other  establishments  and  are  then 
united  in  the  final  process.  The  diagram  of  the  productive  proc- 
ess and  of  the  locations  of  its  stages  appears  in  Figure  37.  In 
short,  we  have  found  a  general  solution.  There  is  just  one  sig- 
nificant limitation:  our  solution  holds  good  only  for  stages  of 
production  which  combine  two  materials  only.  Such  stages  have 

Fig.  37 

triangles  for  their  locational  figures.  This  limitation  is  regret- 
table in  principle,  but  it  is  not  as  important  as  it  might  seem. 
For  it  will  seldom  occur  that  stages  of  production  which  involve 
:omplicated  processes  of  combination  will  follow  each  other.  And  172 
Duly  where  several  such  complicated  stages  of  production  follow 
Dne  another  will  there  be  failure  to  determine  their  location  by 
j:he  use  of  the  expedients  we  have  developed  thus  far.  In  all 
Dther  cases  we  shall  always  be  able  to  construct  the  circles  upon 
which  the  locations  of  the  simpler  stages  of  production  lie  (cf. 
:he  adjoining  Figure  38  in  which  M4C  shows  this  circle  for  such 
m  adjoining  simple  stage  of  production.  This  makes  it  possible 
:o  find  the  line  (Px—P\)  upon  which  the  location  of  the  more 



complicated  preceding  stage  of  production  will  lie.  We  can  find 
this  line  by  using  the  frame  of  Varignon^  for  the  purpose  of  mov- 
ing one  corner  of  the  more  complicated  locational  figure  along 
the  circle  of  the  location  of  the  adjoining  stage  in  production). 
Through  this  method  we  have  a  fairly  far-reaching  general  way 
of  determining  both  locations.  A  special  construction  for  partic- 
ular cases  can  of  course  be  made  with  the  expedients  of  higher 
mathematics,  even  if  the  complications  are  much  greater.  But 
we  shall  limit  ourselves  to  the  finding  of  general  rules. 

Another  aspect  of  the  foregoing  conclusions  is  of  interest 
here.  The  simple  diagram  by  which  we  can  generally  determines 

Fig.  38 

Fig.  39 

the  locations  of  split  production  also  affords  us  a  more  precis« 
answer  for  the  question  as  to  wheji  this  split  will  occur.  Thai 
mathematical  analysis  of  the  Appendix  (cf.  Appendix  I,  §  11) 
shows  that  the  spHt  will  not  occur,  if  the  circles  determining  thö 
locations  of  the  stages  intersect  and  if  at  the  same  time  the  de- 
termining straight  line  goes  through  that  segment. 

But  this  is  not  theoretically  significant,  applying  as  it  doesi 
173  only  to  certain  geographical  situations;  rather,  it  is  the  conse- 
quence of  an  accidental  proximity  of  the  material  deposits  of 
the  different  stages.  Obviously,  no  split  will  take  place  when  thai 
intersecting  point  of  the  determining  straight  line  is  situated  in 
^  Cf.  Appendix,  p.  229. — Editor.  ; 


the  common  segment ;  for  the  intersecting  points  go  beyond  each 
other  (cf.  the  foregoing  Figure  39).  The  elements  of  two  stages 
of  production  remain  next  to  each  other  after  having  met.  A 
common  location  within  the  segment  is  the  result. 


It  is  quite  interesting  that  the  construction  we  discussed  be- 
fore suffices  for  determining  the  locations  even  if  the  splitting 
of  the  productive  process  involves  a  change  of  the  material 
deposits  because  of  the  employment  of  new  deposits.  Such  re- 
placement of  old  deposits  by  new  ones  will  always  occur  when 
the  material  deposits  of  the  last  stages  are  situated  nearer  the 
place  of  consumption,  or  when  material  deposits  of  the  first 
stages  are  situated  nearer  the  deposits  of  the  main  materials — 
nearer  than  is  true  of  the  deposits  which  would  be  most  advan- 
tageous within  the  locational  figure  of  the  unsplit  production. 
The  adjoining  Figure  40  shows  what  will  happen  in  these  cases. 
The  deposit  M'2  has  been  substituted  in  the  first  stage,  while  the 
deposit  M's  has  been  substituted  in  the  second  stage,  because 
these  deposits  are  more  advantageous  for  the  split  production 
than  Mo  and  M3,  which  were  most  advantageous  for  the  unsplit 
production.  One  can  see  at  a  glance  that  the  finding  of  the  loca-  1 74 
tions  of  the  separate  stages  of  production  is  not  complicated  by 
these  substitutions.  We  construct  in  accordance  with  our  former 
rules,  using  the  new  deposits  as  bases. 

This  is  true  even  if  a  material  which  was  formerly  supplied 
for  the  unsplit  production  by  one  deposit  is  now  brought  into  the 
production  of  the  different  stages  from  different  deposits,  inas- 
much as  it  enters  into  the  production  at  several  stages.  A  fre- 
quent example  is  coal.  The  splitting  of  production  simply  neces- 
sitates the  substitution  of  these  different  deposits,  which  then 
become  the  basis  of  our  constructions,  as  outlined  before.  No 
particular  difficulties  ensue  from  that. 




Let  us  suppose  next  that  an  industry  is  oriented  toward  labor 
in  its  productive  process  or  in  parts  of  it.  What  will  be  the  effect 
if  such  an  industry  is  split  up  and  oriented  at  the  locations  of 
the  stages  of  production? 

If  that  industry  is  already  dissolved  into  stages  of  produc- 
tion by  transport  orientation  (which  is  after  all  the  basis  of 


Fig.  40 

Fig.  41 

labor  orientation)  the  location  of  each  stage  may  then  be  re- 
garded as  the  location  of  a  separate  process  of  production.  Lo- 
cation will  be  influenced  by  the  labor  locations  of  the  particular 
stage  according  to  the  rules  which  we  know  already.  Deviation 
will  occur  if  the  labor  location  lies  inside  the  critical  isodapane 
of  the  respective  locational  figure  of  the  stage,  etc.  And  if  de- 
viation does  take  place,  the  deviation  point  is  substituted  for  the 
transport  location.  By  becoming  the  location  of  its  particular 
stage  this  deviation  point  will  influence  the  locational  figures 
of  the  adjoining  stages.  The  construction  of  the  locations  of  the 
stages  will  in  consequence  be  simplified;   for  a  fixed  and  de- 



termined  corner  will  be  substituted  in  the  locational  figure  of  the 
stage  for  an  unknown  comer  which  must  be  found  by  construc- 

The  labor  location  will  consequently  alter,  not  only  the  lo- 
cation of  its  own  stage,  but  also  the  locations  of  the  stages  pre- 
ceding and  following.  For  these  are  not  fixed;  they  are  in- 
fluenced mutually,  each  by  every  other.  The  locations  of  the  175 
adjoining  stages  will  orient  themselves  in  accordance  with  the 
labor  location  between  them,  as  is  indicated  in  the  foregoing 
Figure  41  which  illustrates  a  productive  process  having  two 
stages,  in  which  the  labor  deviation  influences  the  second  stage. 
Due  to  this  deviation,  some  cost  of  transportation  will  be  saved 
(P\P'2  is  shorter  than  PiP'2,  which  otherwise  would  have  had  to 
be  used).  This  circumstance  increases  the  possibilities  of  de- 
viation somewhat  beyond  the  scope  which  could  be  inferred  from 
the  critical  isodapane  around  the  locational  figure  of  that  stage. 

I  do  not  believe  it  is  necessary  to  discuss  further  the  small 
alteration  which  this  involves.  It  is  more  important  to  note  that 
in  this  case  also  former  material  deposits  may  be  replaced  by 
others  more  favorably  located.^  In  a  split  production  this  may 
mean  the  elimination  of  locations  of  entire  stages  of  production 
and  their  replacement  by  locations  which  are  based  upon  entirely 
different  material  deposits  which  happen  to  be  nearer  the  at- 
tracting labor  locations.  Under  certain  circumstances  this  may 
mean  a  considerable  revolution  in  the  entire  set  of  locations  of 
the  stages  of  production — all  due  to  the  labor  deviation  of  just 
one  stage.  But  this  replacement  of  material  deposits  does  not,  of 
course,  create  any  difficulties  of  construction.  Theoretically  its 
effect  is  of  course  exactly  the  same  as  that  of  replacing  material 
deposits  within  an  unsplit  productive  process:  the  attracting 
force  of  the  labor  locations  will  be  strengthened  in  exact  propor- 
:ion  to  the  savings  of  costs  of  transportation  which  result  from 
5uch  replacements. 

*  Cf.  supra,  p.  113  f. — Editor. 


We  ought  to  mention,  finally,  that  labor  deviation  itself 
may  cause  productive  processes  to  split  by  causing  the  deviation 
of  some  location  which  had  previously  followed  the  location  of 
176  the  adjoining  stage.  This  may  be  an  effect  of  labor  deviation 
which  is  superficially  quite  striking,  but  it  does  not  contain  any 
theoretical  problem. 


On  the  basis  of  what  has  been  said  we  may  determine  what 
it  will  mean  if  we  include  the  factors  of  agglomeration  in  our  con- 
siderations. We  are  dealing  in  principle  with  the  same  problems 
which  we  encountered  when  dealing  with  the  deviations  caused 
by  labor  orientation. 

A  separate  function  of  agglomeration  exists  for  every  stage 
of  production  and  it  influences  that  stage  separately.  This  in- 
fluence will  be  exerted  according  to  the  general  rules  of  agglom- 
eration.® The  creation  of  centers  of  agglomeration — as  is  well 
known — is  subject  to  the  creation  of  segments  of  the  sets  of 
isodapanes  of  the  locational  figures  of  the  stages  of  production 
which  have  possibilities  of  agglomeration. 

As  in  the  case  of  labor  deviation,  a  problem  is  created  by 
the  fact  that  wherever  agglomeration  actually  occurs  there  may 
occur  also  a  deviation  of  the  locations  of  those  stages  of  produc- 
tion which  precede  and  which  follow  the  stage  within  which  ag- 
glomeration has  occurred.  But  what  has  been  said  in  dealing! 
with  this  problem  in  the  case  of  labor  deviation  holds  true  also 
for  the  case  of  agglomerative  deviation,  mutatis  mutandis.  How- 
ever, this  problem  will  be  of  much  smaller  significance  than  the 
one  created  by  the  replacement  of  those  material  deposits  which  1 
are  more  unfavorably  situated  than  hitherto  unused  material  de- 
posits lying  much  nearer  the  new  location  created  by  agglomera- 
tion. This  is  due  to  the  fact  that  the  strengthening  of  the  attract- 
ing force  of  the  deviation  points  is  much  more  important. 

*  Cf .  infra,  p.  246.— Editor. 


The  most  important  problem  which  remains  over  and  above 
those  questions  which  we  encountered  in  the  case  of  labor  de- 
viation consists  in  the  fact  that  the  'Vhere"  of  the  point  of 
agglomeration  will  be  altered  when  the  locational  figures  upon 
which  this  point  of  agglomeration  is  based  are  altered.  But  we 
have  seen  before^°  that  the  center  of  agglomeration  shifts  also 
when  the  productive  process  is  not  split.  It  will  be  remembered 
that  this  is  due  to  the  elimination  of  bad  material  deposits.  What 
has  been  said  there  holds  true  here:  the  center  of  agglomeration 
remains  determined  by  the  location  of  the  places  of  consumption 
and  of  the  most  advantageous  material  deposits,  and  does  not 
shift  very  much.  Consequently  no  further  discussion  of  this  177 
problem  is  needed. 

This  brings  us  to  the  end  of  our  theoretical  analysis  of  the 
nature  of  orientation  as  related  to  the  possible  stages  of  a  given 
productive  process.  Following  our  usual  procedure,  our  next 
question  is:  upon  what  conditions  does  this  nature  of  orientation 
within  the  productive  process  depend,  and  how  will  the  known 
changes  of  reality  affect  it? 



The  fact  that  the  locations  of  an  industry  are  split  is  the 
upshot  of  its  technical  nature.  The  splitting  seems  therefore  to 
depend  solely  upon  the  general  characteristics  of  that  industry 
and  to  be  entirely  independent  of  environmental  conditions  such 
as  the  level  of  transportation  costs  and  the  density  of  population. 
Indeed,  it  is  determined  by  the  nature  of  the  productive  process; 
and  any  changes  in  that  nature  will  also  change  the  nature  of 
the  split.  Speaking  more  precisely,  the  technical  nature  of  the 
productive  process  of  an  industry  and  the  manner  in  which  it  is 
handled  will  determine  whether  that  productive  process  has 
technically  independent  parts  and  what  materials  are  available 

^°  Cf .  p.  141,  supra. — Editor. 


for  each  of  these  parts.  It  will  further  determine  how  the  inde- 
pendence of  the  parts  and  the  availability  of  materials  are  af- 
fected by  the  general  economic  development.  The  several  loca- 
tional  figures  are  created  and  altered  by  these  facts. 

We  may  say  in  general  terms  that  the  splitting  of  an  industry 
is  facilitated  when  more  materials  are  used  and  when  these  addi- 
tional materials  are  used  in  several  independent  stages  of  pro- 
duction. No  necessity  to  split  on  the  basis  of  rates  of  transporta- 
tion will  exist  for  an  industry  which  has  a  whole  series  of  inde- 
pendent stages  of  production,  of  which  however  only  the  first 
stage  involves  combining  several  materials,  while  all  the  later 
stages  involve  only  the  additional  application  of  labor.  The  pic- 
ture in  this  case  will  show  the  location  of  the  first  stage  near 
the  materials,  while  the  location  of  all  the  remaining  stages 
will  be  somewhere  along  the  way  between  the  location  of  the  first 
stage  and  the  place  of  final  consumption.  As  a  matter  of  fact, 
these  remaining  locations  will  almost  always  be  situated  at  the 
1 78  place  of  consumption,  due  to  advantages  of  the  market  (Absatz). 
In  spite  of  the  great  number  of  possible  independent  stages  of 
production,  the  productive  process  will  be  split  into  only  two 
stages,  which  we  may  call  the  stage  of  materials  and  the  stage  of 
consumption.  We  find  this  as  the  typical  picture  in  all  those 
older  and  simpler  industries  which  are  carried  on  without  the 
use  of  coal  in  the  higher  stages.  But  if  materials  enter  into  one 
or  more  of  the  later  stages  of  production,  independent  locational 
figures  and  fixed  independent  locations  will  come  into  existence. 
It  should  be  noted,  however,  that  only  the  entrance  of  weight  ma- 
terials, such  as  coal  and  coarse  materials,  will  really  prolong  the 
series  of  locations.  For  the  entrance  of  a  pure  material  or  of  an 
ubiquity  has  the  effect  of  pushing  the  production  toward  the 
place  of  consumption,  and  consequently  does  not  alter  the  orig- 
inal picture.  The  use  of  coal  in  the  higher  stages  of  production  is 
of  necessity  the  main  factor  through  which  the  modern  develop- 
ment stimulates  the  sphtting  of  production — if  it  does  so  at  all. 


But  it  would  be  a  mistake  to  say  that  the  tendency  of  a  given 
industry  to  spHt  increases  in  proportion  to  the  loss  of  weight  of 
raw  materials  within  the  higher  or  later  stages  of  its  production. 
For  even  the  slightest  loss  of  weight  of  an  entering  material 
creates  the  basis  for  an  independent  stage  of  production  with  a 
separate  location,  as  far  as  cost  of  transportation  is  involved. 
The  magnitude  of  this  loss  of  weight  does  not  in  principle  affect 
this  situation  in  the  least.  What  it  does  determine  is  the  extent  to 
which  the  location  of  that  stage  of  production  will  be  attracted 
by  the  deposit  of  the  material  involved.  If  the  material  entering 
the  higher  stages  of  production  is  coal,  this  attraction  may  be  so 
strong  as  to  reunite  the  separate  stages  at  the  coal  deposit. 

These  few  sentences  concerning  the  extent  to  which  the 
splitting  of  production  depends  upon  the  extent  to  which  ma- 
terials enter  into  the  productive  process  do  not  exhaust  the 
discussion  of  the  conditions  surrounding  this  splitting  process. 
This  spHtting  will  be  determined  by  the  nature  of  the  productive 
process  only  to  the  extent  that  transportation  costs  enter.  But 
we  have  seen  that  splits  may  also  be  caused  by  deviation  due  to 
labor  or  to  agglomeration.^^  To  the  extent  to  which  these  devia-  1 79 
tions  are  possible  and  occurring,  splits  are  dependent  upon  the 
conditions  to  which  these  two  kinds  of  orientation  are  subject. 
Splitting  of  these  parts  of  the  productive  process  which  have  not 
formerly  been  separated  is  dependent  particularly  upon  costs  of 
transportation  and  density  of  population,  since  these  two  factors 
as  environmental  conditions  codetermine  labor  orientation  and 
agglomerative  orientation.  For  example,  the  manufacture  of 
linen  clothes  (Wäsche) ,  which  was  formerly  deviated  to  certain 
jlarge  labor  locations,  experiences  at  the  present  time  a  split 
which  is  moving  the  intermediate  stage  of  embroidering  such 
cloth  (for  the  German  manufacture)  as  far  as  Madeira.^-  It  is 
obvious  that  the  split  which  has  occurred  in  this  instance  is  due 

"  Cf .  supra,  pp.  184  f.,  186  f. 
"Written  in  1909. — Editor. 


partly  to  the  lowering  of  costs  of  transportation,  a  decisive  fac- 
tor. We  must  say  a  few  words  regarding  these  general  tenden- 


We  have  said  before  that  the  technical  nature  of  the  pro- 
ductive process  and  its  execution  will  fundamentally  determine 
whether  the  various  groups  of  industries  are  organized  into 
stages  of  production,  and  if  so,  in  what  manner.  Nothing  could 
be  more  erroneous  than  to  assume  that  the  technical  differentia- 
tion of  the  medieval  trades,  from  which  we  shall  start  in  our 
analysis  of  actual  development,  was  inconsiderable.  There  ex- 
isted that  structure  of  technical  stages  of  production  which  re- 
sulted as  a  matter  of  course  from  the  traditional  tools  which  have 
been  the  common  property  of  Euro- Asiatic  civihzations  {vor- 
derasiatisch-europäischer Kultur  kr  eis).  These  tools  split  the 
productive  process  into  about  as  many  technically  independent 
parts  as  it  can  conceivably  contain.  For  these  tools  became  sc 
specialized  that  they  made  it  impossible  to  control  more  than  a 
very  small  part  of  the  productive  process,  and  they  consequentl> 
tore  it  to  pieces  technically.  The  productive  process  througl: 
which  the  metals,  wood,  leather,  and  the  fibers,  as  well  as  mosi 
food  materials,  had  to  pass  was  always  long  and  had  many  inde- 
pendent stages.  It  is  true,  however,  that  two  things  are  typica 
of  the  medieval  economic  system.  First,  the  economic  organi- 
zation which  was  superimposed  on  this  technically  split  produc- 
1 80  tion  was  not  split  to  any  considerable  extent.  The  number  oi 
successive  stages  of  production  which  achieved  economically 
independent  organization  remained  small.^^  There  were  seldorr 
more  than  two  or  three.  Second,  even  those  stages  of  productior 
which  had  become  economically  independent  generally  remained 
together  at  the  place  of  consumption.  No  local  splits  into  loca- 
tions of  the  stages  of  production  followed  the  inconsiderable 

'^  Cf .  regarding  this  point  the  well-known  article  of  Bücher,  "Gewerbe,"  m 
the  Handwörterbuch  der  Staatswissenschaften,  Vol.  III. 


3conomic  splits  of  production.  It  is  well  known  that  the  preven- 
;ion  of  too  numerous  successive  stages  of  production  (as  well  as 
;heir  retention  at  the  market  of  the  town)  was  a  necessary  part 
)f  the  economic  policies  of  medieval  towns. 

But  what  made  possible  these  policies  of  grouping  all  the 
;echnically  independent  parts  of  production  around  the  market 
)f  the  town?  Obviously  the  fact  that  the  technical  potentialities 
:or  splitting  production  did  not  yet  jorce  production  to  split  geo- 
graphically. All  these  individual  and  separate  parts  of  the  pro- 
iuctive  processes  were  largely  oriented  toward  consumption, 
ust  as  we  found  the  inseparable  units  of  medieval  crafts  oriented 
oward  consumption. 

To  the  extent  to  which  they  were  not  oriented  toward  con- 
mmption,  the  policies  adopted  for  the  purpose  of  concentrating 
ndustries  within  the  town  limits  jailed.  Indeed,  we  can  com- 
Dletely  understand  the  development  of  the  larger  part  of  medie- 
/al  rural  trades  (Landgewerbe)  only  if  we  conceive  of  these 
:rades  as  ''stages  of  production."  The  trade  policies  of  the  towns 
iailed  with  regard  to  these  rural  trades  because  these  policies 
:ould  not  overcome  the  locational  rules  according  to  which  these 
stages  were  oriented  toward  their  materials  and  not  toward  con- 
sumption. Consequently  the  concentrating  policies  of  the  towns 
lever  attempt  to  inclose  within  the  town  walls  the  foundries; 
-hese  have  always  been  oriented  toward  the  material  deposits. 
Similarly,  the  towns  did  not  attempt  to  draw  to  themselves  the 
growing  glassworks ;  these  were  oriented  toward  the  fuel  mate- 
*ials.  And  when  later  (since  the  fourteenth  century)  water  power 
s  increasingly  introduced  into  production  and  thereby  increases 
:he  materialization^*  of  initial  and  intermediate  stages  of  produc- 
:ion,  then  these  stages  of  production — the  iron  works,  the  copper 

"We  mean  by  "materialization"  the  extent  of  the  use  of  localized  mate- 
•ials  which  strengthen  the  components  of  the  materials  in  our  locational  figures. 
The  change  from  ubiquitous  to  localized  materials  means  also  "materiahzation." 
^n  view  of  this  circumstance  the  Middle  Ages  had  little  "materiaUzed"  industrial 
production  on  account  of  the  extensive  use  of  ubiquitous  materials  like  wood. 


works,  the  rolling  mills,  and  the  paper  mills — follow  those  other 
stages  of  production  which  have  already  been  taken  outside  the 
towns,  and  they  do  so  in  spite  of  the  concentrating  poHcies  of  the 
i8i  towns. 

It  is  simply  the  slight  materialization  of  medieval  production 
which  causes  the  inconsiderable  locational  differentiation  of  the 
stages  of  production. 

It  is  interesting  to  analyze  how  further  development  leads 
to  further  splitting  of  the  productive  process.  From  our  point 
of  view  the  large  textile  industries  organized  under  the  putting- 
out  system  in  the  fifteenth  and  sixteenth  centuries  represent  mi- 
grations of  industry  away  from  the  place  of  consumption,  their 
large-scale  production  supplementing  or  even  destroying  the  old 
handicrafts'  production.  Spinning  and  weaving  are  separated 
from  tailoring,  which  remains  oriented  toward  consumption, 
while  the  former  migrate  to  locations  of  lowest  costs  of  labor. 
Obviously,  from  the  standpoint  of  our  theory  changed  environ- 
mental conditions,  and  not  technical  conditions,  eliminate  the 
old  locational  unit  of  the  handicraft  production.  Those  parts  of 
the  productive  processes  which  become  organized  according  to 
the  putting-out  system  migrate  to  locations  which  have  become 
more  attractive  because  of  the  general  improvement  in  transpor- 
tation together  with  the  increasing  density  of  population — the 
latter  producing  local  labor  surplus  with  ensuing  possibilities  for 
decreasing  labor  costs. 

The  third  great  period  of  revolution,  from  the  second  half 
of  the  eighteenth  century  until  the  end  of  the  nineteenth  century, 
increases  further  the  dispersion  of  the  locations  of  the  stages  of 
production.  This  is  the  time  when  the  old  mercantilist  industries 
operated  under  the  putting-out  system  and  the  handicrafts  them- 
selves were  gradually  mechanized  to  such  an  enormous  extent. 
The  zigzag  course  of  production  increases  when  mechanized 
182  spinning  is  torn  from  mechanized  weaving;  when  the  mechan- 
ized wood-planing  and  refining  factory  pushes  itself  in  between 


the  sawmill  and  the  manufacture  of  various  finished  products; 
when  the  mechanical  manufacture  of  legs  appears  between  tan- 
nery and  shoe  and  boot  manufactures;  when  the  manufacture 
of  pulp  comes  into  being  as  a  separate  stage  of  paper  manufac- 
ture; when  the  mechanization  of  the  manufacture  of  metals 
quite  generally  puts  the  factory  of  half-finished  products  (of 
the  parts  of  locks,  of  watches,  of  automobiles,  etc.)  between  the 
production  of  the  raw  materials  and  that  of  the  finished  prod- 
ucts; in  short,  when  everywhere  the  mechanization  of  produc- 
tion creates  new  stages  of  production  which  have  independent 

There  can  be  no  doubt  that  the  mechanization  and  capitali- 
zation of  production  has  done  just  that  during  the  time  of  the 
great  industrial  revolution  of  the  nineteenth  century,  thereby 
creating  the  impression  that  the  productive  processes  were  in- 
creasingly split  by  division  of  labor  and  oriented  independently. 
It  is  hardly  doubtful,  either,  that  this  process  has  served  as  the 
basis  for  the  superficial  doctrine  of  the  "international  division  of 
labor,"  which  is  so  closely  connected  with  the  doctrine  of  free 
trade.  It  will  be  remembered  that  by  this  doctrine  we  were  made 
to  believe  that  the  parts  of  the  productive  processes  which  were 
given  an  independent  existence  by  the  increasing  division  of  la- 
bor would  quite  freely  move  to  their  optimal  locations,  and  that 
like  parts  would  concentrate  at  these  places,  as  if  no  transporta- 
tion costs  were  involved  which  would  bind  them  locationally  and 
which  should  therefore  first  be  consulted  regarding  the  locational 
distribution  of  these  parts  of  the  productive  processes.  Econo- 
mists observed  how  the  productive  processes  were  differentiated 
by  the  division  of  labor;  they  made  no  distinction  between  spe- 
cialization and  differentiation  into  stages  of  production;  they 
observed  the  independent  local  orientation  of  the  stages;  and 
since  the  idea  of  the  division  of  labor  had  in  general  become  the 
great  pillow  on  which  all  economists  went  to  sleep,  we  rested  (as 
far  as  the  theory  of  location  was  concerned)  upon  the  idea  of 


the  geographical  or  international  division  of  labor,  a  beautiful 
idea,  perhaps,  but  rather  devoid  of  real  meaning. 

At  present  every  glance  into  life  makes  us  feel  that  the  entire 
concept  of  a  continual  separation  of  new  parts  of  the  productive 
process — a  concept  based  upon  the  law  of  the  division  of  labor- 
is  really  explaining  a  transitory  stage  which  is  followed  by  g 

183  quite  different  and  contrary  development.  We  are  today  face  tc 
face  with  the  fact  that  the  capitalization  and  mechanization  ol 
the  industrial  processes  have  entered  upon  the  contrary  develops 
ment  of  concentration.  If  mechanization  has  in  a  certain  sensi 
differentiated  the  productive  process  into  its  smallest  parts  ir 
order  to  subject  these  parts  to  its  force  and  to  give  them  theii 
appropriate  form,  that  same  mechanization  is  now  gathering 
these  mechanically  well-organized  parts  into  units.  Mechaniza 
tion  thus  introduces  through  enormous  concentrations  a  new  ane 
quite  as  gigantic  a  revolution  in  industrial  locations.  Thesi  i 
processes  of  concentration  are  first  of  all  concentrations  of  capjc 
ital.  They  need  not  affect  the  technical  and  organizational  in 
dependence  of  the  combined  parts  of  production;  they  couli 
let  the  former  structure  of  the  stages  of  production  and  thai 
locations  remain  intact.  But  there  exist  as  a  matter  of  fact  man} 
connecting  links  between  the  tendencies  of  capital  to  concen 
träte  and  the  tendencies  of  technique  to  organize — links  th» 
discussion  of  which  would  lead  us  much  too  far  afield  at  thi; 
time.  But  it  can  be  said  at  once  that  the  concentration  of  cap 
ital  is  creating  for  the  concentration  of  organization  and  techni 
cal  process  new  frameworks  which  will  gather  together  produc 
tive  processes  which  had  previously  been  independent.  Every 
one  knows  of  the  development  in  the  iron  industry;  the  onc( 
independent  processes  of  mining  the  ore,  producing  and  rolling 
the  steel,  have  been  gathered  into  one  undivided  process.  Then 
are  many  parallel  developments,  which  are  perhaps  less  striking 

184  but  not  less  effective.  The  manufacturer  of  worsteds  who  ac 
quires  a  spinning  mill  and  attempts  to  combine  it  with  his  weav 


ing  factory,  the  hardware  manufacturer  who  combines  all  the 
different  parts  of  production  as  they  had  grown  up  under  the 
putting-out  system;  the  gun-factory  which  includes  all  stages 
of  production  from  the  raw  material  to  the  finished  product — 
all  these  are  specific  instances  of  a  general  development.  Every- 
where the  accumulations  of  capital  stand  behind  these  technical 
and  organizational  combinations  as  their  larger  framework.  The 
structure  of  the  stages  of  production  is  simplified  and  the  split- 
up  parts  group  themselves  together  again.  New  'Vocational 
units"  are  created  which  sometimes  include  whole  series  of  in- 
dustries. These  new  units  must  orient  themselves  anew  accord- 
ing to  their  "locational  weight,"  "labor  coefficient,"  and  "coeffi- 
cient of  manufacture"  resulting  from  the  combinations.  The 
necessity  of  an  entirely  new  orientation  may  remain  hidden  dur- 
ing  the  beginnings  of  the  development;  certain  strong  plants 
may  simply  attract  other  stages  of  production  and  thus  become 
centers  of  crystallization.  The  foundry  may  attract  the  rail- 
roHing  mill  or  the  forge  works;  the  iron  forge  may  attract  as 
large  a  foundry  or  as  large  a  hardware  factory  as  seems  suitable. 
But  even  this  beginning  may  mean  locational  alterations  of  a 
very  noticeable  kind;  it  may  cause  the  total  or  partial  stagna- 
tion of  industrial  districts  which  are  losing  the  parts  of  the  pro- 
ductive process  in  which  they  had  specialized. 

But  this  is  not  the  end  of  the  story.  In  the  long  run  the  move- 
ment will  not  end  with  such  attractions  of  parts  or  stages  of 
production  to  the  stronger  points  of  crystallization.  That  is  to 
say,  in  the  long  run  the  movement  will  continue  until  it  per- 
meates the  entire  industry.  In  the  long  run,  then,  there  must 
come  about  a  fundamentally  new  orientation  of  the  new  large 
units  of  production  which  have  been  created  by  these  combina- 
tions. This  new  orientation  may  come  about  slowly,  because  of  18; 
the  enormous  fixed  capital  which  is  involved  in  a  dislocation  of 
these  industrial  giants  and  which  give  great  weight  to  their  lo- 
cation as  it  developed  historically.  But  this  new  orientation  must 


sometime  take  place  if  location  is  at  all  controlled  by  economic 
laws,  and  it  will  push  the  new  units  to  the  locations  which  are 
determined  by  their  locational  weight,  their  labor  coefficient, 
and  their  form  coefficient.  This  will  complete  the  locational  revo- 
lution which  was  started  by  the  recent  development  toward  con- 
centration. During  the  entire  nineteenth  century  we  were  under 
the  influence  of  a  revolution  in  locations,  a  revolution  which, 
starting  with  the  unity  and  simplicity  of  handicraft  organization, 
eventuated  in  the  extremely  chaotic  orientation  of  independently 
organized  large-scale  industries  of  the  old  style.  Today  we  are 
at  the  beginning  of  a  new  revolution  which  may  lead  us  to  a 
new  and  much  more  simple  orientation,  to  units  of  locations  of 
large-scale  industries  organized  in  combinations. 



We  have  proceeded  thus  far  on  the  assumption  that  the  vari- 
ous processes  of  industrial  production  are  independent  of  each 
other  without  any  relationship  to  one  another.  This  is  not  the 
case.  They  in  fact  interact  upon  one  another  in  various  ways.  It 
remains  to  discuss  this  interaction.  It  may  be  of  three  kinds: 

First,  the  production  of  quite  different  articles  may  be  com 
bined  in  one  plant  {Betrieb).  This  is,  from  our  viewpoint,  a  lo 
cal  coupling  of  independent  industrial  processes. 

Second,  the  locally  separate  production  of  various  articlesfk 
may  be  based  upon  the  same  set  of  materials  and  unfinished 
products.  Here  we  have  a  connection  through  materials  of  the 
1 86  preliminary  stages  of  several  different  industrial  processes. 

Third,  the  product  of  one  industry  may  enter  another  indus- 
try without  being,  as  in  the  previous  case,  material  or  unfinished 
product,  but  rather  "means  of  production"  or  "auxiliary  prod- 
uct" (for  example,  wrapping  material).  This  may  be  described 
as  market  connection  of  one  industry  with  one  or  several  others. 



If  products  of  different  productive  processes — and  since 
each  product  has  theoretically  its  own  process,  we  may  simply 
say,  if  different  products — are  produced  in  the  same  plant^^ 
this  may  be  due  to  either  technical  or  economic  reasons.  It  is 
possible  that  for  technical  reasons  several  products  of  different 
kinds  must  be  produced  at  the  same  time,  as  for  example  in 
certain  chemical  industries.  But  this  technical  necessity  may  be 
absent.  The  factory  which  produces  cables,  accumulators,  and 
other  electrical  apparatus,  the  garment  factory  which  manufac- 
tures overcoats,  capes,  shawls,  blouses,  etc.  at  the  same  time, 
does  so  for  economic,  and  not  for  technical  reasons.  This  dif- 
ference is  rather  significant  in  general  as  well  as  for  location. 
I  The  coupling  of  productive  processes  which  results  from  a 
«connection  of  technical  factors  makes  one  location  for  several 
kinds  of  product  imperative.  It  may  be  regarded  as  the  bifur- 
cation of  a  unitary  process  of  production  at  the  place  of  produc- 
tion. Not  one,  but  several,  places  of  consumption  influence  the 
location;  and  from  our  discussion  of  agglomerated  production 
we  know  the  influence  and  significance  of  several  places  of  con- 
sumption. We  know  that  the  existence  of  several  places  of  con- 
sumption does  not  seriously  complicate  the  determining  of  the 
location.  True,  we  must  take  the  components  of  several  places  187 
of  consumption  into  account  when  considering  the  orientation 
of  this  type  of  production.  The  locational  figure  which  results 
has  several  components  of  consumption,  their  number  depend- 
ing upon  the  number  of  kinds  of  product.  These  components 
must  be  weighted  with  the  weights  corresponding  to  the  kinds 
of  products.  That  is  all.  The  locational  figure  of  an  isolated  unit 
of  production  will  look  somewhat  like  Figure  42  (next  page)  for 
plants  which  combine  two  kinds  of  production.  The  location  will 
then  be  determined  according  to  the  general  rules. 

^°By  plant  (Betrieb)  we  do  not  mean  enterprise,  since  an  enterprise  does 
not  need  to  be  confined  to  a  local  unit  of  manufacturing. 


One  might  think  that  the  same  situation  would  arise  when 
the  coupling  was  technically  not  necessary.  Without  doubt  the 
locational  figure  which  is  finally  created  will  be  quite  similar. 
But  it  will  be  created  in  an  entirely  different  way,  and  has 
therefore,  locationally  speaking,  quite  another  meaning.  This 
locational  figure  of  the  coupled  processes  will  always  involve  a 
deviation  by  which  those  processes  will  be  moved  away  from  the 
location  which  they  occupied  when  they  were  isolated,  except  in 
the  unusual  instance  in  which  the  coupled  processes  have  the 
place  of  consumption  and  the  material  deposit  in  common.  Ob- 
viously the  coupled  productive  processes  would  have  had  dif- 
ferent locational  figures  and  different  minimum  points  if  their 

Fig.  42 

material  deposits  and  places  of  consumption  were  different.  If 
their  production  is  actually  coupled,  a  deviation  from  those 
minimum  points  must  have  taken  place.  This  kind  of  coupling, 
then,  will  follow  the  rules  of  deviation  which  we  have  found  for 
the  labor  orientation  and  for  the  agglomerative  orientation  of 
industries,  and  it  must  be  analyzed  accordingly.  This  analysis 
may  be  determined  by  the  special  nature  of  labor  deviation  asi 
well  as  by  that  of  agglomeration. 

It  may  happen  that  the  coupling  of  several  productive  proc 
esses  at  the  new  location  takes  place  because  this  location  hasi 
a  labor  supply  which  renders  certain  savings  possible  for  each 
of  these  processes.  The  particular  skill  of  these  laborers  may, 
for  example,  protect  these  industries  better  against  the  evil  ef- 
fects of  business  cycles  or  changes  of  fashion.  This  really  con- 
stitutes no  peculiar  problem.   Such  labor  locations  are  points 


toward  which  the  several  processes  will  deviate;  such  locations 
will  attract  these  processes  according  to  the  influence  which  their 
index  of  savings  has  for  each  process.  As  we  have  seen,^^  this 
influence  will  be  determined  by  the  respective  labor  coefficients. 
The  elimination  of  unfavorable  material  deposits,  the  increase 
of  the  attracting  force  of  large  locations,  all  this  will  take  place 
according  to  the  rules  which  we  know.  The  only  difference  is 
that  each  place  attracts  several  productive  processes  of  differ- 
ent kinds,  and  not  processes  of  an  identical  kind.  We  need 
therefore  to  analyze  the  way  in  which  these  processes  are  in- 
fluenced separately.  That  is  simple. 

The  other  case  seems  more  complicated.  It  may  happen 
that  the  coupling  of  productive  processes  and  the  deviation 
which  it  entails  are  due  to  agglomerative  forces.  Coupling  takes 
place  because  through  such  a  connection  of  productive  processes 
it  is  possible  to  eke  out  advantages  which  are  unattainable  by 
divided  production.  These  advantages  may  be  due  to  organiza- 
tion, to  the  use  of  machinery,  to  wholesale  buying  and  selling — 
any  or  all  of  which  the  separate  processes  did  not  permit  on  ac- 
count of  their  small  size.  A  unit  of  agglomeration  made  up  of 
several  industries  will  come  into  existence.  This  unit  of  ag- 
glomeration will  be  determined  by  a  function  of  economy  or  a 
function  of  agglomeration^^  which  is  related  to  several  industries 
instead  of  being  related  to  one.  There  is  nothing  peculiarly  diffi- 
cult about  the  question  of  how  this  function  of  economy  agglom- 
erates the  individual  productive  processes  of  the  industries  in- 
volved. We  merely  apply  the  rules  which,  as  we  have  found, 
determine  the  formation  of  segments  by  the  isodapanes.  The 
difference — the  new  element — is  that  the  isodapanes  of  several 
different  industries  are  involved. 

But  the  application  of  the  general  formula  of  agglomeration 
seems  to  be  rather  difficult.  This  difficulty  would  in  turn  render 
difficult  the  understanding  of  the  final  orientation  of  such  com- 

'®  Cf.  supra,  p.  no  f.— Editor.  "  Cf.  pp.  126,  246.— Editor. 


bined  production.  It  seems  that  we  shall  have  to  apply  the  sev- 
eral functions  of  agglomeration  of  the  several  industries.  But 
although  this  formula  is  a  theoretical  makeshift  (as  we  have  oft- 
en emphasized),  a  solution  is  not  as  difficult  as  may  at  first  sight 
189  appear.  In  our  formula  of  agglomeration  we  shall  have  to  sub- 
stitute the  f(M)  (the  function  of  agglomeration)  of  the  com- 
bined productive  process  and  its  locational  weight  (A).  If  we 
ask  which  tendencies  of  agglomeration  does  any  one  of  these 
products  follow,  the  theoretical  answer  is  twofold.  If  the  prod- 
ucts are  all  produced  separately,  they  will  follow  the  tendencies 
which  are  indicated  by  their  individual  formula;  if  they  are 
produced  in  combination  or  coupled  with  others,  they  will  follow 
the  tendencies  which  are  indicated  by  the  formula  of  agglomera- 
tion of  the  combined  process.^^  But  generally  this  complicated 
formula  will  not  be  necessary  for  the  arbitrary  combination  of 
several  different  productive  processes  in  the  same  plant  (plant, 
not  enterprise;  cf.  foregoing)  will  as  a  rule  be  profitable  only 
provided  similar  kinds  of  labor,  of  machinery,  or  of  materials 
are  used  for  the  different  products. ^^  This  means  that  arbitrary 

^^The  meaning  of  the  text  is  not  certain  here.  It  reads:  ".  .  .  .  Wenn  sie 
alle  getrennt  produziert  werden,  den  und  den,  die  sich  aus  der  einfachen  Formel 
ergeben;  wenn  kombiniert,  mit  den  und  den  anderen  produziert  wird,  den  und 
den,  die  sich  aus  der  Kombinationsiormel  ergeben."  It  is  likely,  from  what  is 
said  in  this  paragraph  as  well  as  in  previous  chapters,  that  this  sentence  refers 
to  the  following  problem :  Will  a  given  productive  process,  under  the  influence 
of  various  agglomerative  tendencies,  enter  an  agglomeration  which  does  not 
involve  a  coupling  of  it  with  other  productive  processes,  or  will  it  enter  a  unit 
of  agglomeration  which  does  involve  such  coupling?  It  must  be  supposed  that 
some  of  the  agglomerative  tendencies  referred  to  issue  from  a  unit  or  units  of 
agglomeration  which  do  not  involve  the  coupling  of  the  several  productive  proc- 
esses which  are  being  attracted;  while  other  tendencies  issue  from  a  unit  or 
units  of  agglomeration  which  do  involve  such  couphng.  The  answer  to  this 
problem,  following  as  it  does  from  comparison  of  the  two  or  several  formulas, 
seems  to  be  indicated  in  the  text. — Editor. 

"  The  situation  is  of  course  quite  different  where  coupling  is  technically 
necessary.  In  this  case  it  is  quite  usual  for  the  products  which  emerge  from  the 
same  materials  to  require  quite  different  kinds  of  machinery  and  labor.  But  it 
would  not  be  worth  while  to  combine  two  products  which  are  essentially  dis- 


combination  can  take  place  only  if  a  productive  process  has 
the  same  function  of  agglomeration  and  the  same  material  index 
no  matter  whether  it  agglomerates  the  productive  processes  of 
one,  or  of  another,  or  of  several  of  the  products.  We  do  not  have 
to  distinguish,  roughly  speaking,  between  the  agglomerating 
processes  of  isolated  and  of  coupled  productions.  The  formula 
of  agglomeration  of  the  one  is  identical  with  that  of  the  other. 

This  consideration  of  the  arbitrary  coupling  of  productive 
processes  yields  a  rather  important  by-result.  The  density  of 
production,  it  will  be  remembered,  must  be  taken  into  account  190 
in  considering  the  probable  extent  of  agglomeration  of  a  pro- 
ductive process  in  reality;  it  must  be  entered  into  the  formula 
of  agglomeration.  This  density  of  production  must  be  deter- 
mined from  the  amount  of  space  required  by  all  the  productive 
processes  within  a  given  area  which  are  similar  to  each  other 
and  may  be  coupled  and  combined  into  units  of  agglomeration. 
For  this  amount  of  space  apparently  determines  which  agglom- 
erations either  of  separate  productive  processes  or  of  coupled 
processes  will  come  into  existence  in  reality.  That  this  is  true 
will  hardly  need  further  proof  after  all  that  has  been  said;  but 
it  is  probably  the  most  important  result  which  the  foregoing 
analysis  yields,  supplementing  the  general  theory  of  location. 


Independent  productive  processes  may  be  connected  by  the 
materials  which  they  use,  and  such  connection  may  be  due  either 
to  technical  or  economic  factors.  Productive  processes  are 
technically  connected  if  the  material  of  one  process  is  the  by- 

similar  in  these  particulars  unless  such  combination  were  technically  necessary, 
since  neither  a  more  intensive  use  of  the  machinery,  nor  of  labor,  nor  wholesale 
buying  of  materials  could  be  achieved — all  of  which  means  that  the  most  impor- 
tant savings  of  agglomeration  are  absent.  As  a  matter  of  fact  only  these  two 
forms  exist  in  reality :  Technically  necessary  coupling  of  partly  differing  produc- 
tive processes,  and  arbitrary  couphng  of  loosely  related  productive  processes. 
Concerning  by-products,  cf .  infra. 


product  of  the  second  main  product  of  any  one  of  the  stages  of 
another  process.  For  example,  the  woolen  industry  is  connected 
with  certain  lines  of  the  leather  industry  through  its  materials, 
because  leather  branches  off  as  a  second  main  product  of  one  of 
the  initial  stages  of  the  production  of  wool.  Similarly,  the  dye- 
stuff  industry  is  connected  with  other  industries  using  coke, 
because  coal  tar  (upon  which  the  dye-stuff  industry  is  based)  is 
a  by-product  of  the  burning  of  coke.  Productive  processes  are 
economically  connected  by  their  materials,  if  a  given  raw  ma- 
terial, or  a  given  unfinished  product  may  be  used  either  for  the 

Common  Raw  Material  ^^^ 

Fig.  43 

one  process  or  for  the  other.  This  case  is  very  frequent.  Our  mod- 
ern industrial  structure,  enormously  differentiated  by  innumera- 
ble branches  functioning  as  independent  productive  processes, 
is  rooted  in  a  few  raw  materials  which  it  is  not  very  difficult  to 
enumerate.  In  other  words,  large  parts  of  this  industrial  struc- 
ture are  connected  by  materials,  since  groups  of  raw  materials, 
such  as  wood,  metals,  soils,  leather,  etc.,  may  be  used  alternative- 
ly by  the  different  parts. 

The  effect  of  these  two  kinds  of  connection  through  mate- 
rials (technical  connection  and  economic  connection)  is  in  no 
191  way  the  same. 

Each  individual  productive  process  connected  for  technical 
reasons  with  another  productive  process  through  a  material  will 
at  a  certain  place  join  the  other  process  (cf.  the  adjoining 
schema.  Figure  43).  If  the  materials  of  the  different  industries 
as  they  come  into  existence  at  the  junction  show  a  distinct  order 


of  rank,  i.e.,  if  one  of  these  materials  is  the  main  material  while 
the  others  are  distinctly  by-products,-*^  or  even  waste,  the  result- 
ing problem  of  orientation  is  simple.  The  process  whose  mate- 
rial is  the  main  material  is  the  controlling  one,  and  the  common 
initial  stage  will  be  oriented  toward  the  location  of  this  process. 
The  resulting  location  is  the  material  deposit  of  the  other  indus- 
tries which  use  the  by-product.  There  remains  no  problem. 

But  a  problem  does  remain  if  all  the  products  which  are  pro- 
duced at  the  junction  point  are  of  importance  from  a  locational 
point  of  view  (this  being  either  due  to  their  weight  or  to  their 
value,  cf.  the  last  footnote).  In  this  event  this  connected  stage  192 
is  a  part  of  several  equally  important  or  similarly  important 
processes  of  production;  it  has  therefore  two  or  more  lines  of. 
production  continuing  it.  All  of  these  lines  of  production  influ- 
ence the  location  of  the  junction  point  which  is  their  common 
initial  stage  of  production.  Consequently  the  location  of  this 
junction  point  is  not  apparent  without  further  analysis.  The  so- 
lution is  the  same  as  in  the  reverse  case,  in  which  two  or  more 
different  series  of  productive  processes  are  united  into  one  prod- 
uct by  a  process  of  combination.  We  need  only  imagine  the  fig- 
ure which  was  given  on  page  181  to  be  applied  in  reverse  geo- 
graphical position  in  order  to  see  how  the  common  initial  location 
(which  is  here  substituted  for  the  common  final  location  there), 
and  the  succeeding  locations  of  the  several  series  of  productive 
processes  will  influence  each  other. 

^  They  may  be  by-products,  because  they  are  very  inferior  in  weight,  al- 
though equal  in  value.  In  that  case  they  do  not  have  any  effect  whatever  upon 
the  location  of  the  junction  point  because  their  determinant  is  too  weak.  Thus 
wool  does  not  appreciably  influence  the  orientation  of  the  co-product,  leather, 
although  wool  is  a  second  and  valuable  product  of  the  tannery,  or  may  be  such 
at  least.  On  the  other  hand,  by-products  may  become  trifling  influences  because 
they  are  greatly  inferior  in  value,  if  not  in  weight.  They  would  have  to  have  an 
effect  upon  the  location  if  they  would  not  be  eliminated  from  consideration  for 
economic  reasons.  This  is  the  case  of  bones  in  the  slaughter-house.  The  location 
of  the  slaughter-house  will  not  be  influenced  appreciably  by  the  realization  of 
the  bones,  because  the  by-product  has,  comparatively,  too  small  a  value. 


Much  simpler  is  on  the  whole  the  case  in  which  different  pro- 
ductive processes  are  connected  by  materials  on  account  of 
economic  reasons.  This  case  is  also  much  more  important  be- 
cause it  permeates  the  entire  industrial  structure.  Theoretically 
we  have  to  start  from  the  idea  of  individual  productive  processes, 
as  that  idea  has  always  been  used  so  far.  The  transport  orienta- 
tion of  the  individual  process,  in  which  materials  are  used  which 
may  be  used  alternatively  in  other  and  different  processes,  will 
nevertheless  take  place  according  to  the  simple  and  well-known 
rules,  without  regard  to  whether  the  material  may  be  used  in 
other  processes.  The  individual  productive  process  does  not  need 
to  concern  itself — and  therefore  will  not  concern  itself — about 
whether  its  material  will  also  be  used  in  different  productive 
processes,  any  more  than  it  concerns  itself  about  whether  its 
material  will  be  used  in  other  individual  processes  of  the  same 
kind  of  industry.  It  follows  that  the  basic  transport  orientation 
within  the  economic  structure  (from  which  we  always  have  to 
start  in  our  analysis)  will  be  quite  indifferent  to  such  connec- 
tions through  materials.  The  basic  transport  orientation  will 
not  be  affected  by  the  fact  that  iron  is  today  an  important  raw 
material  in  several  hundred  different  series  of  productive  proc- 
esses and  will  be  supplied  to  these  series  from  the  same  deposits. 
193  The  same  is  true  of  wood,  leather,  etc.  The  groundwork  of  loca- 
tions as  determined  by  the  costs  of  transportation — considered 
for  the  time  being  apart  from  its  alteration  due  to  agglomeration 
and  labor — will  not  be  affected  by  whether  a  hundred  different 
kinds  of  productive  processes  will  use  one  and  the  same  material 
from  the  same  material  deposit,  or  whether  they  will  use  a  hun- 
dred different  raw  materials  which  happen  to  come  from  one  and 
the  same  deposit.  The  different  processes  become  internally  in 
no  way  dependent  upon  one  another  because  they  all  use  the 
same  raw  material;  they  merely  happen  to  have  the  same  geo- 
graphical starting-point,  nothing  more. 

The  importance  of  the  possibility  of  such  a  common  geo- 



graphical  starting-point  becomes  apparent  only  when  we  con- 
sider that  agglomeration  and  labor  orientation  influence  the 
transportational  groundwork.  But  no  new  locational  problem  is 
created,  at  that.  Just  as  agglomeration  and  labor  orientation 
will  create  locations  of  common  orientation  for  the  initial  stages 
of  the  same  industry,  so  they  will  create  such  common  orienta- 
tion for  those  stages  of  different  industries  which  use  the  same 
material  or  half-finished  product.  The  result  is  the  same  as  in 
the  first  case.  The  individual  stages  of  production,  which  be- 
long to  different  succeeding  processes  of  production  (i.e.,  be- 
long to  different  industries),  will  agglomerate  according  to  the 
same  rules  and  in  the  same  way  as  those  stages  which  are  the 
initial  stages  of  the  same  kind  of  production.  It  is  of  importance 
for  this  agglomeration  that  the  different  processes  be  rooted  in 
the  same  place  and  therefore  He  near  one  another,  but  nothing  of 
theoretical  significance  can  be  said  about  it.  However,  it  is 
probably  fortunate  that  the  picture  of  the  originally  isolated 
orientation  of  the  different  productive  processes  connected  in 
fact  through  their  materials  and  the  picture  of  their  agglomera- 
tion according  to  our  general  rules  will  render  lucid  and  simple 
the  apparently  very  complicated  problem  of  how  the  orientation 
of  these  different  processes  is  interrelated  within  the  industrial 
structure.  The  entire  industrial  structure  is  permeated  by  such 
"economic"  connections  through  material;  and  it  seems  at  first 
almost  impossible  to  consider  the  orientation  of  an  individual  in- 
dustry in  isolation  and  to  define  rules  for  it,  since  a  great  many 
other  industries  seem  to  influence  its  orientation.  Still,  such  194 
isolated  consideration  and  analysis  is  seen  to  be  possible  and 
admissible  now  that  we  have  seen  that  the  "economic"  interre- 
lations through  materials  create  only  secondary  alterations  of 
the  groundwork  of  the  transport  orientation — an  orientation 
which  is  built  up  upon  the  basis  of  the  isolated  processes  of  pro- 
duction and  is  quite  independent  of  such  economic  interrela- 


tions.-^  These  deviations  take  place  according  to  the  same  rules 
that  would  be  operative  if  the  entire  industrial  organism  were 
one  single  and  uniform  industry.  I  believe  that  an  understanding 
of  these  considerations  will  justify  the  manner  in  which  our 
entire  theory  is  built  up — using,  as  it  does,  an  isolating  analysis 
of  the  individual  industries  or  even  of  the  individual  process  of 


As  stated  before,  the  product  of  an  industrial  process  may 
enter  into  another  industrial  process  without  being  used  as  ma- 
terial or  half-finished  product;  it  may  be  a  fixed  means  of  pro- 
duction or  an  auxihary  product.  The  new  situation,  as  compared 
with  the  cases  studied  thus  far,  is  constituted  by  the  fact  that 
the  two  industrial  processes  are  no  longer  connected  by  a  com- 
mon place  of  production.  Instead,  they  are  connected  by  the 
fact  that  the  one  productive  process  creates  places  oi  consump- 
tion for  the  other;  this  situation  exists  v^here  they  are  connected 
through  some  means  of  production.  Or  they  are  connected  by 
the  fact  that  a  common  market  is  created  (where  for  example  the 
main  product  and  the  wrapping  material  are  brought  together) ; 
this  situation  exists  where  the  processes  are  connected  through 
some  auxiliary  product.  Neither  of  these  situations  can  be  called 
"a  connection  of  production"  since  there  takes  place  no  trans- 
formation of  materials  which  would  create  new  products.  No 
organic  connection  of  the  two  productive  processes  takes  place. 
The  connection  is  based  solely  upon  the  linking  of  the  market  of 
the  one  with  the  other. 

This  connection  may  have  very  important  consequences  in- 
fluencing the  location  at  which  the  means  of  production  or  the 
auxiliary  product  are  produced,  quite  apart  from  the  fact  that 
the  locations  of  these  productive  processes  are  in  any  event  in- 
fluenced by  the  places  of  consumption  created  by  the  main 

^  These  rules  have  been  elaborated  for  the  deviations  due  to  labor  and  ag- 
glomeration, as  set  forth  in  chaps,  iv  and  v. — Editor. 



process.  It  may  be,  and  often  is,  the  case  that  the  manufacture 
of  the  means  of  production,  or  of  the  auxiliary  product,  will  be 
drawn  toward  the  location  of  the  main  process  so  strongly  as  to 
become  united  with  that  main  process.  If  this  occurs  in  ac- 
cordance with  our  general  rules  of  location  (i.e.,  because  the  195 
locations  within  the  locational  figure  of  the  auxiliary  process 
are  situated  at  the  place  of  consumption,  thus  following  their 
material  index)  then  this  situation  contains  nothing  theoretically 
remarkable.  The  locations  of  the  production  of  the  main  indus- 
try are  the  locations  of  the  auxiliary  industry  simply  because 
the  former  are  the  places  of  consumption  of  the  latter.  But  if  the 
auxiliary  process  is  drawn  to  the  location  of  the  main  process 
for  special  reasons  (for  example,  because  the  auxiliary  industry 
needs,  on  account  of  the  nature  of  its  product,  local  contact  with 
the  production  of  the  main  process — which  happens  for  example 
often  in  the  manufacture  of  machinery),  then  a  special  situation 
seems  to  arise.  But  may  it  be  emphasized  at  once,  no  real  prob- 
lem appears.  All  we  can  say  here  is  that  special  locational  fac- 
tors— and  such  special  factors  will  often  interfere  with  the  rules 
of  the  theory — will  draw  the  location  of  the  auxiliary  industry 
to  the  place  of  consumption  although,  according  to  the  general 
rules,  it  should  lie  elsewhere.  As  the  place  of  consumption  is 
definitely  given  by  the  main  industry,  nothing  remains  unde- 

It  may  be  well  to  indicate  here  that  without  doubt  special 
locational  factors  have  extensive  application  to  the  production  of 
such  means  of  production  and  of  auxiliary  products.  In  fact, 
these  special  factors  are  the  very  ones  which  make  the  nature  of 
these  industries  as  auxiliary  industries  quite  apparent  even  at  a 
cursory  glance.  But  it  should  be  emphasized  that  whether  or  not 
such  a  connection  of  the  places  of  production  is  caused  by  such 
special  locational  factors,  the  fact  will  not  at  all  alter  the  funda- 
mental locational  nature  of  these  industries.  An  industry  manu- 
facturing machines  will  remain  an  industry  connected  with  the 


market  or  consumption  place  of  its  main  industry,  and  this  is 
true  whether  its  locations  are  drawn  to  its  places  of  consump- 
tion (say,  the  locations  of  the  main  industry)  or  whether  it 
orients  itself  within  its  own  locational  figure  according  to  the 
general  rules.  It  would  be  quite  wrong  to  narrow  the  definition 
of  an  auxiliary  industry  by  requiring  the  existence  of  such  local 
contact.  Any  industry  which  is  connected  with  a  main  industry 
196  by  its  market  is  an  auxihary  industry. 

The  only  instance  in  which  such  market  connection  yields 
anything  for  our  general  theory  occurs  when  the  location  of  the 
main  process  is  affected.  This  is  possible;  the  necessity  for  lo- 
cal contact  may  cause  the  main  process  (if  at  a  certain  stage 
it  needs  certain  kinds  of  machinery)  to  tend  toward  the  loca- 
tions of  such  machinery,  for  there  it  would  find  opportunities 
for  easy  and  dependable  repair  and  such  stimulus  to  further 
technical  development  as  would  result  from  local  contact.  In 
that  case  the  main  process  may  perhaps  deviate  to  the  locations 
of  the  manufacture  of  such  machinery.  But  this  type  of  devia- 
tion is  known  to  us  already;  it  belongs  in  the  category  of  ag- 
glomeration. For  the  machine  factories  on  their  part  will,  for 
the  purpose  of  local  contact,  try  to  find  locations  in  which  they 
are  kept  fully  busy.  These  locations  are  the  units  of  agglomera- 
tion of  the  main  process.  We  have  seen  how  this  local  contact 
with  machine  factories  (cf.  129  supra)  is  one  of  the  factors 
which  create  these  units  of  agglomeration. 

Here,  as  before,  it  may  be  a  bit  difficult  to  see  clearly  the  dy- 
namic working  of  these  forces.  The  want  for  local  contact  is  the 
reason  why  the  machine  industry,  to  stick  to  our  example,  ori- 
ents itself  toward  the  location  of  the  main  process  of  production. 
The  resulting  tendency  to  come  into  contact  can  be  realized,  but 
it  can  be  realized  only  at  locations  having  considerable  produc- 
tion of  this  kind.  This  tendency  also  exists  in  the  case  of  the 
main  process,  and  means  a  saving  for  it;  but  since  such  saving 
appears  only  in  units  of  agglomeration  to  which  it  is  linked  from 


the  other  side,  it  becomes  an  agglomerative  factor  and  therefore 
influences  the  main  industry  according  to  the  rules  of  agglom- 
eration. The  manufacture  of  machines  goes  to  the  places  where 
the  main  industry  agglomerates;  and  the  main  industry  agglom- 
erates there  partly  because  the  manufacture  of  machines  goes 


We  have  given  a  picture  of  the  connecting  links  between  the 
different  industrial  processes  which  are  of  importance  for  loca- 
tions. Apart  from  the  technical  coupling  of  productive  processes 
and  technical  connection  through  materials,  they  all  represent 
merely  secondary  alterations,  if  alterations  at  all,  of  the  ground- 
work of  industrial  orientation  as  built  upon  the  basis  of  theoret- 
ically isolated  branches  of  industry.  All  these  secondary  altera-  lo' 
tions  take  place  according  to  the  general  and  simple  rules  of 
location.  These  alterations  are  in  fact  but  certain  special  aspects 
of  the  familiar  deviations  due  to  labor  and  to  agglomeration, 
and  they  are  subject  to  the  well-known  rules  determining  such 
deviation.  The  two  technical  relations  connecting  productive 
processes  which  really  do  interfere  with  the  groundwork  of 
transport  orientation  both  take  place  according  to  well-known 
rules.  They  really  are  but  one  and  the  same  phenomenon  as  con- 
sidered for  different  stages  of  production.  Their  interference  in 
no  way  destroys  the  general  theoretical  basis  upon  which  our 
analysis  of  orientation  was  built. 

Thus,  this  basis  and  the  rules  developed  from  it  really  em- 
brace quantitatively  and  qualitatively  the  final  and  entire  orien- 
tation of  industry.  Quantitatively,  because  they  cover  industrial 
productions  of  every  kind;  qualitatively  because  they  include  all 
these  productive  processes  in  their  theoretically  isolated  orien- 
tation as  well  as  in  their  final  orientation,  having  regard  to  all 
general  relations  which  affect  them.  We  arrive  at  a  complete 
theoretical  understanding  of  the  final  orientation  if  we  start  with 
the  individual  industries,  if  we  then  come  to  a  clear  understand- 


ing  of  the  points  of  minimal  transportation  costs  for  each  indi* 
vidual  series  of  productive  processes  going  from  the  places  of 
consumption  back  to  the  material  deposits,  and  if  we  finally 
analyze,  according  to  the  rules  of  labor  deviation  and  agglom- 
eration, the  ways  in  which  these  individual  series  are  connected 
with  each  other  and  are  woven  together  into  that  seemingly  very 
complicated  tissue  which  the  modern  industrial  structure  repre- 
sents. All  this,  including  the  connection  between  the  productive 
processes  of  dissimilar  products,  is  theoretically  clear  and  serves 
to  explain  the  development  of  the  comphcated  combinations 
which  we  so  often  encounter  today  in  the  actual  industrial  world 
198  with  its  manifold  goods. 





The  question  now  arises  as  to  what  extent  our  rules  as  devel- 
oped so  far  will  determine  the  local  distribution  of  all  the  units 
of  industrial  production  within  the  definite  geographical  limits 
of  a  country.  This  question  is  by  no  means  answered  by  all  that 
has  been  said  so  far.  It  might  be  that  the  rules  thus  far  evolved 
determine  the  local  distribution  of  production  in  all  its  com- 
ponent parts  as  dependent  upon  one  another  and  still  leave  open 
the  possibihty  of  production  grouping  itself  in  very  different 
ways  throughout  the  land. 

This  is  in  fact  the  case.  We  shall  try,  therefore,  to  reveal  the 
limits  of  the  pure  theory  of  location  by  placing  the  manufactur- 
ing industries  in  the  setting  of  the  whole  economic  system.  It  is 
obvious  that  our  previous  discussion  can  give  a  definite  picture 
of  the  orientation  of  industry  only  upon  the  basis  of  the  hypoth- 
eses upon  which  it  was  built.  It  will  be  remembered  that  these 
conditions  were  fourfold,  namely,  ( i )  that  the  location  and  the 
size  of  the  places  of  consumption  are  given  as  fixed;  (2 )  that  the 
location  of  the  material  deposits  is  given;  (3)  that  the  location 
of  the  labor  locations  is  given;  (4)  that  the  labor  supply  at  these 
latter  is  unlimited  at  constant  cost.^  If  these  hypotheses  be  al-  199 
lowed,  the  theory  as  stated  so  far  will  positively  determine  the 
location  of  each  particle  of  industrial  production.^ 

^It  will  be  observed  that  this  involves  the  assumption  of  a  (only  theoretic- 
Uy  possible)  complete  mobility  of  labor.  The  foregoing  passages  have  been 
somewhat  changed  from  the  original  in  order  to  recall  as  clearly  as  possible 
vhat  has  gone  before. — Editor. 

^  In  the  original  the  following  methodological  observation  is  inserted  at  this 
joint :  "It  is  no  flaw  in  the  theory  that  the  picture  which  is  created  thereby  is 
lependent  upon  certain  other  factors,  such  as  transportation  rates,  density  of 


But  these  hypotheses  should  now  be  subjected  to  analysis. 
The  location  and  the  size  of  the  places  of  consumption  are  from 
the  viewpoint  of  locational  theory  no  more  given  than  are  the 
locations  and  the  wage  level  of  labor.  Nor  is  the  location  of  the 
200  material  deposits,  at  least  of  the  agricultural  ones,  so  given. 
On  the  contrary,  these  are  matters  which  are  determined  to  a 
certain  extent,  or  perhaps  completely,  by  the  prevailing  loca- 
tional conditions.  For  that  reason  they  cannot  be  presupposed 
in  a  theory  of  location;  rather  they  ought  to  be  explained.  We 
must  get  behind  this  assumption  that  they  are  given,  because  it 
was  only  justified  as  an  aid  in  our  analysis.  An  attempt  to  look 
behind  this  assumption  will  show  whether  the  theory  as  devel- 
oped thus  far  suffices  to  explain  industrial  location,  or  whether 
it  has  perhaps  gaps  which  must  be  filled  by  another  approach. 

"To  analyze  the  elements  which  were  assumed  as  given' 
involves  an  analysis  of  our  locational  rules  as  they  will  actuall> 
operate  within  the  living  economic  system  as  a  whole.  There 
appears  at  once  before  our  imagination  the  picture  of  a  circle  ol 
forces  which  it  seems  hardly  possible  to  break  through.  The  lo 
cations  of  the  places  of  consumption,  the  labor  locations,  and  th( 
material  deposits,  which  supposedly  determine  the  orientatior 
of  industries,  are  themselves  resultants  of  this  very  same  in 

population,  locational  weight  of  the  industries,  and  the  indices  of  value  addec 
through  manufacture  and  of  labor  costs.  The  introduction  of  these  factors  doe; 
not  detract  from  the  completeness  of  the  theory ;  for  these  factors  are  indeed  'giv- 
en' from  the  viewpoint  of  locational  theory.  They  are  subject  to  rules  which  an 
distinct  and  independent  of  locational  theory.  Transportation  rates  and  materia 
indices  are  a  resultant  of  the  general  technical  development,  while  the  indices  ol 
labor  costs  and  of  value  added  through  manufacture  are  partly  a  resultant  of  thl' 
development  and  partly  a  resultant  of  the  general  development  of  economic  or- 
ganization and  industrial  technique.  The  density  of  population  and  of  produc- 
tion also  has  its  roots  outside  of  the  locational  sphere,  at  any  rate  in  the  general 
form  in  which  it  figures  as  a  determining  factor  in  our  theory  so  far  (namely,  ai 
the  general  ratio  between  the  size  of  the  population  or  of  the  amount  of  prod- 
ucts demanded  and  the  area).  In  all  these  conditions  we  do  not  assume  anything 
which  the  theory  itself  ought  to  explain."  (This  is  slightly  abbreviated.) — Editor 


dustrial  orientation.  For  each  particle  of  industrial  production 
which  moves  to  a  certain  place  under  the  influence  of  locational 
factors  creates  a  new  distribution  of  consumption  on  account  of 
^the  labor  which  it  employs  at  its  new  location,  and  this  may  be- 
come the  basis  of  further  locational  regrouping.  Such  a  particle 
of  industrial  production  creates  a  new  basis  for  material  deposits 
which  will  be  used  (or,  in  the  case  of  agricultural  materials,  even 
created),  which  in  turn  will  be  partly  the  basis  of  further  re- 
orientation of  industries. 


I  In  order  to  break  through  this  circle  we  might  say:  each 
Hequilibrium  of  industrial  location  at  a  certain  given  moment  is 
a  modification  of  a  previous  equilibrium,  and  this  modification 
[las  been  necessitated  by  the  development  of  the  general  condi- 
tions of  locational  distribution.  Viewed  from  the  particular 
period,  such  an  equilibrium  would  appear  as  a  rational  trans- 
formation of  a  historically  developed  system  which  had  become 
oartly  irrational  and  was  therefore  transformed.  This  historical  201 
system  of  locations  of  industrial  production,  of  places  of  con- 
sumption, and  of  material  deposits  is  the  given  reality;  and  by 
operating  upon  this  basis,  our  rules  will  determine  the  locations 
according  to  the  development  of  the  general  conditions,  such  as 

[ates  of  transportation,  material  indices,  etc. 
Without  doubt  such  an  assumption  of  a  basis  as  given  in 
ime  rather  than  in  thought  will  be  a  valuable  aid  for  the  investi- 
'gation  of  industrial  locations.  In  no  other  way  will  it  be  pos- 
sible, for  example,  to  analyze  the  locational  developments  within 
:he  German  economic  system  since  1861.  But  it  is  obvious  that 
:his  historical  basis  is  something  entirely  different  from  what 
Ne  are  looking  for  at  present.  This  historical  basis  is  the  ma- 
:erial,  so  to  speak,  which  is  transformed;  whereas  we  are  looking 
'or  a  basis  or  theory  of  this  transformation  itself.  We  want  to 
ind  the  general  basis  upon  which  the  new  system  orients  itself. 
We  have  construed  such  a  basis  thus  far  by  assuming  as  given: 


places  of  consumption,  material  deposits,  and  labor  location. 
Since  nothing  is  to  be  assumed  as  given  for  the  new  system 
which  we  wish  to  analyze,  we  must  try  to  analyze  further  the 
whole  economic  system  itself. 


What  is  the  most  general  force  which  connects  the  different 
parts  of  an  isolated  economic  system  from  the  point  of  view  of 
location?  We  shall  recognize  it  if  we  ask  ourselves  what  force 
determining  location  would  develop  if  some  people  were  to  oc- 
cupy a  new  and  empty  country  for  the  purpose  of  building  up 
such  an  isolated  economic  system.  We  assume,  of  course,  that  its 
local  grouping  will  be  determined  entirely  by  economic  con- 
202  siderations.^ 

Under  such  circumstances  ^'layers"  or  ''strata"  of  locational 
distribution  would  develop.  These  strata  would  be  interrelated, 
i.e.,  they  would  affect  each  other.  It  is  obvious  that  there  must 
be  a  first  stratum  of  local  distribution  of  industries  which  will 
become  the  basis  and  the  starting-point  of  all  further  develop- 
ment as  soon  as  the  (supposedly  limited)  area  of  settlement  is 
chosen.  This  first  stratum  must  be  the  agricultural  stratum, 
whatever  may  be  the  conditions  in  any  other  respect,  and  wheth- 
er or  not  cities  are  at  once  founded ;  for  under  all  circumstances 
the  settlement  of  agricultural  lands  must  take  place  to  an  extent 
sufficient  to  produce  the  necessary  agricultural  products  for  the 
whole  population.  In  order  to  achieve  this  purpose  the  requisite 
part  of  the  population  must  distribute  itself  over  as  large  an  areai 
suitable  for  agriculture  as  is  necessary  for  the  production  of  this 
necessary  amount  of  agricultural  products,  given  the  prevailingi 

'  These  problems  have  recently  been  discussed  from  a  new  and  interesting i 
viewpoint  by  Hans  Ritschl,  "Reine  und  Historische  Dynamik  des  Standorts  der 
Erzeugungszweige,"  Schmoller's  Jahrbuch  (1927),  pp.  813  ff. ;  cf.  also  Introduc- 
tion above,  p.  xxxii. — Editor. 


conditions  of  the  natural  environment,  technique,  and  organi- 
zation.* 203 

This  first  stratum  of  local  distribution — this  settled  area 
with  its  population,  the  agricultural  stratum — represents  the 
geographical  foundation  for  all  other  strata.  It  represents  such 
a  foundation  first  of  all  for  that  part  of  industrial  production 
(the  primary  industrial  stratum,  it  may  be  called)  which  works 
directly  for  it.  The  places  of  consumption  for  all  stages  of  this 
primary  industrial  stratum  are  given  by  the  local  distribution 
within  the  agricultural  stratum.  If  we  recall  our  rules  it  will  be 
evident  that  this  second  stratum  of  local  distribution  (this  pri- 
mary industrial  stratum)  is  oriented  under  the  influence  of  ag- 
riculture. Agriculture  fixes  the  places  of  consumption,  the  ma- 
terial deposits,  and  the  locational  figures. 

But  there  are  a  number  of  other  large  groups  for  which  a 
place  will  have  to  be  found  in  our  structure  of  locational  distri- 
bution: (i)  The  industrial  population  which  is  engaged  in  sup- 
plying the  wants  of  the  primary  industrial  stratum  for  industrial 

*  In  the  original  the  following  observations  are  inserted  here :  "It  does  not 
concern  us  for  the  present  that  this  area  may  be  more  or  less  densely  populated 
and  depending  upon  this  degree  of  density  may  be  somewhat  larger  or  smaller 
as  the  further  strata  of  locational  distribution  (concentration  in  cities,  etc.)  de- 
velop. Both  these  developments  will  take  place  in  accordance  with  the  well- 
known  law  of  Thiinen  about  the  relation  of  the  different  degrees  of  intensity  of 
agricultural  production  and  the  distance  of  that  production  from  the  place  of 
consumption  [Cf.  Johann  Heinrich  von  Thünen,  Der  Isolierte  Staat,  and  above, 
pp.  xix  ff. — Ed.]  It  is  certain  that  some  relation  exists  between  the  number  of 
people  who  want  to  live  in  an  isolated  economic  system  and  the  area  which  is 
needed  for  agricultural  production  (a  certain  natural  environment,  standard  of 
living,  as  well  as  a  development  of  technique  and  organization).  This  ratio  can 
oscillate  only  between  the  Hmits  just  discussed.  It  is  of  course  possible,  and  occurs 
frequently,  that  this  area  of  agricultural  production  is  chosen  partly  with  a  view 
to  advantages  to  other  industrial  production  such  as  that  of  raw  materials.  But 
that  does  not  alter  the  fact  that  the  size  of  this  area  is  the  foundation  of  the  whole 
structure  of  strata  of  locational  distribution.  And  this  size  is  necessitated  by 
the  wants  of  the  whole  system  for  agricultural  products."  This  is  slightly  abbre- 
viated, and  a  footnote  of  the  original  text  is  worked  into  it. — Editor. 


goods;  (2)  the  population  engaged  in  circulating  the  goods  pro- 
duced through  trade  and  transportation;  (3)  that  group  of  the 
population  which  only  consumes,  like  officials,  free  professions, 
persons  living  on  their  own  private  means;  and  finally  (4)  the 
industrial  population  which  supplies  the  wants  of  these  last  two 

The  group  of  industrial  population  supplying  the  primary 
industrial  stratum  is  determined  by  it  just  as  this  latter  stratum 
204  is  determined  by  the  agricultural  stratum.  The  primary  indus- 
try creates  the  geographical  layout  of  the  sphere  of  consump- 
tion and  thus  creates  the  framework  of  the  locational  founda- 
tion. It  should  be  noted,  however,  that  in  a  strict  sense  this 
industrial  stratum  which  is  oriented  under  the  influence  of  the 
primary  industrial  stratum  is  not  a  single  whole,  but  is  itself  di- 
vided into  numerous  substrata.  If  we  assume  that  the  division  of 
labor  is  highly  developed,  we  shall  find  first  a  substratum  which 
is  directly  engaged  in  supplying  the  wants  of  the  primary  indus- 
try; next  we  shall  find  a  substratum  which  is  engaged  in  supply- 
ing the  wants  of  the  foregoing  substratum;  another  one  which 
works  for  this  one;  and  so  on.  There  will  be  a  number  of  sub- 
strata or  layers  (superimposed  on  each  other  and  decreasing  in 
size)  of  which  each  gets  its  sphere  of  consumption  and  therefore 
its  general  locational  foundation  from  the  previous  one.  If  we 
suppose,  for  example,  that  50  per  cent  of  a  people  are  agricul- 
turists while  the  other  50  per  cent  are  engaged  in  industrial 
pursuits  (and  the  country  has  only  the  strata  which  we  have  dis- 
cussed thus  far),  then  obviously  25  per  cent  of  the  population 
will  suffice  for  supplying  the  industrial  products  wanted  by  the 
agriculturists,  since  50  per  cent  suffice  to  do  it  for  the  whole  peo- 

^  Offhand  it  might  be  suggested  that  we  treat  the  domestic  servants  as  a 
special  stratum.  But  from  the  viewpoint  of  locational  analysis  these  people  are  a 
part  of  the  consuming  stratum  to  which  they  belong;  they  do  not  necessitate 
separate  treatment. 


ple.^  In  other  words,  the  primary  industrial  stratum  oriented 
under  the  influence  of  agriculture  will  contain  50  per  cent  of  the 
industrial  population.  For  these  50  per  cent  a  further  25  per 
cent  of  the  industrial  population  must  suffice  to  supply  its  de- 
mand for  industrial  products.  These  2  5  per  cent  are  the  first  sub- 
stratum of  the  secondary  industrial  stratum  oriented  under  the 
influence  of  the  primary  industrial  stratum.  In  turn,  another  12.5 
per  cent  must  suffice  for  supplying  this  first  substratum.  These 
12.5  per  cent  would  then  be  the  second  substratum,  and  for  sup- 
plying their  wants  6.25  per  cent  must  suffice — ^which  would  be 
the  third  substratum.  This  example  illustrates  how  the  indus- 
trial population  is  intertangled  in  substrata  or  layers  of  decreas- 
ing size  and  how  each  substratum  is  the  locational  foundation  of 
the  succeeding  one.  But  we  need  not  concern  ourselves  further 
with  these  interrelations.  The  whole  structure  has  its  founda- 
tion in  the  local  distribution  of  the  primary  industrial  stratum 
oriented  under  the  influence  of  agriculture.  We  shall  treat  these 
substrata  collectively  as  the  third  great  stratum,  the  "secondary 
industrial  stratum"  which  is  oriented  under  the  influence  of  the 
primary  industrial  stratum. 

If  we  now  think  of  this  third  stratum  together  with  the  first 
two  as  one  whole,  we  have  before  us  the  economic  system.  The 
locational  distribution  of  the  largest  part  of  the  remainder  sim- 
ply leans  upon  it.  The  role  of  such  groups  as  have  not  yet  been  205 
discussed  is  simply  one  of  a  proportional  strengthening  of  the 
different  parts  of  this  system. 

This  strengthening  of  the  existing  structure  is  illustrated  by 
all  those  parts  of  the  population  which  attend  to  the  actual  ship- 
ping of  material  goods  from  one  location  to  another  (the  retail 
traders  and  the  transportation  agencies),^  and  thus  handle  the 

®  This  seems  to  presuppose  an  equal  amount  of  consumption  per  individual 
throughout,  that  is,  an  equal  standard  of  living  as  far  as  industrial  products  are 
concerned.  Otherwise  the  foregoing  statement  would  not  hold  good. — Editor. 

'^  Cf .  Introduction  above,  p.  4. 


process  of  circulation.  Similarly,  the  large  body  of  officials  with 
local  functions  represent  merely  a  strengthening  of  the  existing 
locational  distribution.  These  officials  are  distributed  largely 
according  to  the  general  distribution  of  population,  and  are 
therefore  from  a  locational  viewpoint  only  exponents  of  it.  This 
whole  mass  of  local  tradesmen  and  functionaries  need  not  be 
differentiated  from  our  previously  discussed  strata  at  all.  If  one 
wishes  to  separate  them,  however,  one  may  think  of  them  as  a 
local  organizing  stratum,  for  purposes  of  classification. 

A  really  independent  stratum  is  made  up  of  the  other  parts 
of  the  population  engaged  in  the  circulating  process  and  the 
groups  which  only  consume.  Of  the  former  this  stratum  would 
include  all  those  who  are  engaged  in  the  general  organization  and 
managements  of  the  exchange  of  goods,  whether  material  or  im- 
material; of  the  latter  it  would  include  those  officials  who  do  not 
have  local,  but  general,  organizing  functions — the  liberal  pro- 
fessions and  those  persons  living  on  their  private  means.  All 
these  persons  show  tendencies  of  stratification  totally  different 
from  those  of  the  local  organizing  stratum.  They  seem  to  be 
quite  free  in  the  choice  of  their  locations.  They  appear  to  be  ele- 
ments of  the  economic  system  very  little  subject  to  economic 
causes  in  their  choice  of  their  locations,  as  in  the  case  of  persons 
living  on  their  private  means,  intellectuals,  artists;  or,  if  they 
are  subject  to  economic  causes,  such  causes  operate  upon  them 
in  a  very  complex  way  and  are  mixed  with  other  causes  (as  is  the 
case  of  officials  in  the  central  government  and  wholesale  trad- 
206  ers).  But  be  that  as  it  may,  what  primarily  interests  us  here  is 
the  fact  that  the  locational  distribution  of  these  elements  is 
something  separate  and  independent.  If  they  are  oriented  in  re- 
lation to  the  economic  system  at  all,  they  are  oriented  in  relation 
to  it  as  a  whole  and  as  it  is  created  by  the  three  or  four  previous- 
ly mentioned  strata.  Although  their  stratification  is  of  varying 
types  and  subject  to  quite  varying  rules,  they  belong  in  one 
group  in  the  sense  that  their  stratification  can  only  take  place 


upon  the  foundation  of  all  the  other  strata  we  have  discussed 
before.  We  shall  refer  to  this  group  under  the  term  "central  or- 
ganizing stratum." 

There  remain  those  parts  of  the  population  which  supply 
the  wants  of  the  last  two  strata,  the  organizing  strata,  as  we  have 
called  them.  These  parts  of  the  population  will  be  partly  indus- 
trial and  partly  either  local  organizing  strata  or  central  organ- 
izing strata.  Superimposed  on  these  there  are  the  industrial  and 
other  substrata  supplying  the  groups  just  mentioned,  which  in 
turn  possess  their  dependent  substrata,  and  so  on.  These  groups 
telescoping  each  other  ad  infinitum  do  not  need  to  concern  us. 
For  we  need  only  separate  out  those  substrata  depending  upon 
the  central  organizing  stratum,  since  the  substrata  depending 
upon,  and  following,  the  local  organizing  stratum  will  merely 
contribute  to  the  existing  local  distribution,  for  that,  as  we  have 
seen,  is  precisely  what  the  local  organizing  stratum  does.  But 
the  stratum  depending  upon  the  central  organizing  stratum  con- 
stitutes the  fifth  stratum,  which  we  shall  call  the  "central  de- 
pendent stratum."  Its  substrata  consist  of  industrial  units  inter-  207 
spersed  with  local  and  central  organizing  groups.  But  we  may 
ignore  the  central  organizing  groups  as  numerically  not  impor- 
tant, while  the  local  organizing  elements  are  to  be  thought  of 
as  strengthening  further  the  industrial  units.  For  purposes  of 
practical  analysis  we  may  treat  this  entire  group  collectively  as 
one  single  stratum  the  locations  of  which  are  determined  by  the 
industries  it  contains  and  are  dependent  upon  the  central  organ- 
izing stratum. 

We  have  now  found:  (i)  the  agricultural  stratum,  (2)  the 
primary  industrial  stratum,  (3)  the  secondary  industrial  stra- 
tum, (4)  the  central  organizing  stratum,  (5),  the  central  de- 
pendent stratum.  The  local  organizing  stratum  is  embraced  in 
the  first  three  as  a  strengthening  element.  These  strata  afford  us 
a  systematic  understanding  of  the  whole  mechanism  of  stratifi- 


cation — an  understanding  which  is  sufficient  for  practical  pur- 

The  locational  forces  which  connect  the  different  strata  play 
back  and  forth  from  the  upper  strata  to  the  lower,  as  well  as 
from  the  lower  to  the  upper  ones.  The  location  of  the  centers 
based  upon  the  non-agricultural  strata  creates  the  places  of  con- 
sumption for  agricultural  production;  around  these  places  of 
consumption  the  agricultural  production  groups  itself  in  circles, 
as  Thünen  has  shown.^  This  formation  of  circles  creates  not 
only  a  certain  geographical  distribution  of  the  kinds  of  agricul- 
tural production,  but  also  a  distribution  of  the  agricultural  pop- 
ulation, since  the  agricultural  population  ranges  itself  according 
to  the  intensity  of  production.  In  so  doing  these  circles  change 
to  a  certain  extent  the  foundation  of  the  whole  pyramid  of  strata. 
This  causes  one  of  those  rounds  of  interdependent  forces  which 
make  the  analysis  of  economic  life  such  a  thorny  task.  When  we 
come  to  the  empirical  analysis  we  shall  have  to  take  up  this  prob- 
lem created  by  these  changes  of  the  foundation  of  the  pyramid 
208  of  strata  and  of  their  quantitative  importance.  All  that  I  wish  to 
show  now  is  that  these  changes  do  not  destroy  the  theoretical  jus- 
tification of  the  locational  structure  which  we  have  erected.  It 
should  be  remembered  that  such  changes  are  after  all  only  a  re- 
action. The  formation  of  such  circles  can  only  follow  an  already 
existing  and  definite  stratification  of  the  economic  system  along 
the  hues  which  we  have  suggested.  Speaking  more  strictly,  it 
must  have  been  preceded  by  the  choice  of  some  area  as  the  foun- 
dation of  the  economic  system.  This  foundation  must  have  been 
chosen  as  the  agricultural  basis  within  which  the  settlements  of 
the  non-agricultural  population  are  afterward  fixed.^  It  is  im- 

^  Cf .  above,  pp.  xix  ff. 

"  It  may  be,  as  was  said  before,  that  the  economic  advantages  of  these  non- 
agricultural  settlements  have  been  decisive  in  the  choice  of  the  area.  But  that 
does  not  alter  the  fact  that  they  are  only  an  incidental  factor  decisive  in  choosing 
the  area  as  a  whole,  but  not  the  primary  factor  in  the  process  of  its  stratification. 


possible  to  conceive  of  this  '^reaction"  as  anything  but  a  sec- 
ondary phenomenon,  although  it  is  true  that  Thiinen  did  assume 
the  city  as  the  unexplained  basic  phenomenon  of  the  distribution 
of  agricultural  locations.  We,  on  the  other  hand,  wish  to  clarify 
as  far  as  possible  just  where  and  how  cities  develop.  For  this 
purpose  we  must  go  beyond  the  reaction  of  this  growth  of  the 
city  upon  the  distribution  of  the  agricultural  population;  we  are 
forced  to  analyze  in  the  foregoing  manner  the  process  of  strati- 


How  far  does  this  locational  structure  substitute  real  data 
for  construed  ones  and  thus  fix  the  industries  unequivocally  ac- 
cording to  the  rules  which  we  have  found?  Three  construed 
data  had  to  be  replaced  with  real  data:  those  relating  to  places 
of  consumption,  those  relating  to  material  deposits,  and  those 
relating  to  labor  locations  and  their  unlimited  labor  supply  at 
constant  cost  (equal  wage  levels). 

I.  Our  entire  analysis  of  the  mechanism  of  stratification  is 
built  upon  the  idea  of  treating  the  different  strata  as  spheres  of 
consumption  of  their  successors.  The  sphere  of  consumption  is 
therefore  throughout  these  strata  something  given,  although  of 
course  variable  in  the  upper  strata  in  accordance  with  changes 
in  the  lower.  In  most  cases  this  sphere  of  consumption  is  given,  209 
not  as  an  indefinite  geographical  distribution  of  consumption, 
but  rather  as  very  definite  places  with  very  definite  magnitudes 
of  consumption.  Certainly  they  were  treated  as  definite  places  in 
the  elaboration  of  our  theory.  And  the  sphere  of  consumption  is 
in  fact  given  in  this  definite  form  for  all  the  higher  strata,  for 
which  higher  strata  the  places  of  production  of  the  lower  strata, 
as  well  as  the  centers  of  organization  and  trade,  become  places  of 
consumption  of  a  very  definite  magnitude.  And  what  we  have 
just  said  of  the  higher  strata  holds  true  even  for  the  primary  in- 
dustrial stratum  which  is  built  upon  the  agricultural  stratum. 
While  this  is  true,  it  certainly  must  be  conceded  that  there  are 


manifold  agrarian  forms  of  settlement  which  make  for  multi- 
farious structural  developments  of  this  basis  of  consumption; 
and  it  must  furthermore  be  conceded  that  the  connection  be- 
tween this  primary  industrial  stratum  and  the  underlying  sphere 
of  agricultural  consumption  may  be  very  difficult  to  detect,  be- 
cause the  rather  scattered  agricultural  consumption  cannot  be 
supplied  except  via  the  agglomerations  created  by  industrial  pro- 
duction (cities).  All  these  facts  are  only  extraneous  complica- 
tions which  interfere  with  our  perceiving  that  here  also  we  have 
a  system  (a  very  complex  one)  of  places  of  consumption  having 
a  given  magnitude.  The  industries  will  orient  themselves  in  ac- 
cordance with  this  system  in  exactly  the  same  way  (disregarding 
the  ''reaction"  we  have  discussed  before)  as  they  do  in  the  higher 
strata  where  the  forms  of  distribution  of  consumption  are  more 
clearly  perceivable. 

2.  The  distribution  of  the  material  deposits  takes  place  in 
terms  of  the  system  of  places  of  consumption  according  to  the 
rules  which  the  theory  has  given  for  the  construction  of  the  lo- 
cational  figures  based  upon  the  places  of  consumption  as  a  start- 
ing-point— at  least  this  is  true  of  a  large  part  of  the  material 
210  deposits  which  exploit  deposits  already  in  existence  such  as 
mines  and  the  like.  In  such  cases  the  choice  of  the  material  de- 
posits is  all  that  has  to  be  done,  and  this  has  been  described  in 
the  theory.  But  the  problem  remains  of  how  those  material  de- 
posits are  located  which  are  agricultural  in  nature,  since  in  this 
case  the  "deposits"  themselves  must  be  "created,"  natural  con- 
ditions being  the  only  given  factor. 

If  there  were  no  independent  forces  involved  in  the  distribu- 
tion of  agricultural  production,  the  answer  to  this  question  would 
be  simple.  In  that  case  we  could  say  that  the  natural  conditions 
of  production  of  the  materials  are  the  determining  factor,  that 
the  more  or  less  favorable  "natural  conditions,"  in  conjunction 


with  their  location,  would  determine  the  development  of  such 
"deposits"  according  to  the  same  rules  according  to  which  the 
more  or  less  favorable  location  of  the  already  existing  mining 
deposits  determines  their  employment  in  conjunction  with  their 
productivity.  In  both  cases  these  deposits  would  be  given  if  the 
places  of  consumption  were  given.  As  a  matter  of  fact  the  indus- 
trial strata  do  try  to  shape  their  basis  of  agricultural  materials 
in  a  way  analogous  to  their  basis  of  mined  materials,  as  some- 
thing given  by  their  natural  conditions.  But  industry  will  be 
thwarted  in  these  attempts  by  the  inherent  tendencies  of  agri- 
cultural distribution,  which  tendencies  of  course  affect  the  devel- 
opment of  agricultural  production  in  spite  of  the  fact  that  it  is 
the  basis  of  industrial  strata.  In  other  words,  the  economic  con- 
ditions of  agricultural  production  will  become  a  determining 
factor  in  addition  to  those  which  would  be  decisive  if  only  the 
usefulness  of  agricultural  production  as  an  industrial  material 
deposit  were  in  question.  Specifically,  this  involves  its  location 
in  relation  to  the  places  of  consumption  and  in  relation  to  the 
labor  locations  as  well  as  its  rank  among  competing  material  de- 
posits. These  conditions  are  of  course  the  ones  analyzed  by 
Thünen,^°  and  as  we  have  seen  they  are  in  part  secondary  phe- 
nomena of  industrial  stratification  itself.  In  this  case  they  touch 
the  primary  foundation.  This  shows  that  the  actual  develop-  211 
ment  of  these  agricultural  material  deposits  can  only  be  regard- 
ed as  given  provided  this  circular  process  is  introduced  into  our 
analysis,  i.e.,  in  the  empirical  analysis.  But  it  is  important  that 
we  know  these  rules  and  that  we  realize  they  do  not  contain  any- 
thing problematical.  As  said  before,  the  interference  of  the  eco- 
nomic conditions  of  agricultural  production  means  that  the  rules 
as  set  forth  by  Thünen  become  operative.  Each  agricultural 
material  deposit  is  under  competition  from  other  agricultural 
employments  which  would  use  the  soil  for  the  production  of 
different  materials.  The  most  profitable  use  will  be  the  one  un- 

^^  Cf .  above,  p.  xix. — Editor. 


dertaken.  For  our  purposes  this  fact  may  be  expressed  in  the  fol- 
lowing fashion :  each  industry  will  have  as  many  potential  de- 
posits of  the  agricultural  materials  it  needs  as  there  exists  area 
which  is  by  its  nature  capable  of  producing  this  material.  But  it 
will  have  these  potential  deposits  at  very  different  ''prices  at  the 
deposit."  At  each  deposit  the  "price  at  the  deposit"  for  a  certain 
material  is  determined  by  the  necessity  of  displacing  the  (ac- 
cording to  Thiinen's  law)  next  profitable  employment.  Thus 
these  potential  deposits  are  by  this  ''price  at  the  deposit"  placed 
into  the  scale  of  possible  material  deposits  of  their  own  kind 
much  in  the  same  fashion  as  the  deposits  of  mining  materials 
are.  They  will  be  developed  as  bases  of  locations  and  employed 
for  production  according  to  the  rules  we  know. 

The  places  of  consumption  and  the  material  deposits  are 
given  by  the  locational  structure  of  the  economic  system  as  we 
have  analyzed  it.  The  rules  which  determine  them  are  some- 
times quite  direct  and  simple,  sometimes  a  bit  more  complicat- 
212  ed,  but  in  every  case  they  are  quite  unequivocal.  This  means 
that  the  picture  of  the  orientation  of  industry  would  be  revealed 
(within  the  framework  of  the  locational  structure  we  have  ana- 
lyzed) by  the  locational  rules  which  we  have  discovered,  if  this 
orientation  were  independent  of  the  labor  locations  and  of  the 
differences  between  their  wage  levels,  and  were  based  solely 
upon  costs  of  transportation  and  the  "pure"  agglomeration  built 
upon  this  transport  orientation.^^  For  to  the  extent  to  which 
orientation  is  determined  by  these  forces,  only  the  world  of 
places  of  consumption  and  of  material  deposits  comes  under 
consideration  as  the  given  geographical  basis  of  the  real  struc- 
ture. It  would  be  possible  to  calculate  for  each  geographical 
framework  and  for  each  stage  of  general  economic  and  technical 
development  how  the  locational  picture  of  industry  would  shape 
up  provided  the  number  of  population,  the  distribution  of  agri- 
cultural settlement,  and  the  main  distribution  of  the  "central  or- 

-  Cf.  pp.  135  ff. 


ganizing  stratum"  were  known.  There  would  be  no  room  for  the 
influence  which  a  particular  economic  system  (capitalism,  so- 
cialism, or  some  other)  could  exercise  upon  the  basic  locational 
orientation,  since  the  "pure"  rules  would  fix  the  locations  of  in- 
dustry in  a  general  way,  at  least.  The  theoretical  task  would  be 
completed,  and  no  further  "reahstic"  theory  would  be  necessary. 


But  what  will  happen  if  we  take  into  consideration  the  de- 
viations due  to  labor  and  the  labor  orientation  which  rests  upon 
them?  The  discussion  of  these  deviations  has  thus  far  been 
based  upon  the  assumption  that  the  labor  locations  were  given 
and  that  the  differences  in  their  wage  levels  were  constant.  Does 
the  mechanism  of  local  distribution  which  we  have  considered 
thus  far  give  us  any  clues  for  determining  the  local  distribution 
of  such  differences  of  wage  levels,  for  the  causes  creating  the 
labor  locations,  and  finally  for  the  rules  determining  their  devel- 
opment which  have  so  far  been  eliminated  by  the  assumption  of 
an  unlimited  supply  of  labor  at  equal  cost?  Apparently  none 
whatever.  This  is  the  great  gap  in  our  analysis  so  far.  In  the 
rules  determining  the  creation  and  the  development  of  labor  lo- 
cations lies  hidden  the  problem  which  remains  for  a  further  the- 
oretical analysis.  This  problem  will  have  to  be  solved  by  the  213 
"realistic"  theory.  For  at  this  point  it  becomes  necessary  to  con- 
sider particular  economic  systems.  I  do  not  wish  to  assert  that 
the  creation  and  development  of  labor  location  can  be  explained 
by  economic  reasons;  but  if  it  can  be  so  explained  the  reasons 
will  be  related  to  the  position  which  the  particular  economic  sys- 
tem gives  to  labor.  For  apart  from  what  one  calls  (according  to 
Sombart)  an  "economic  system,"  i.e.,  apart  from  the  particular 
determining  form  of  organization  which  the  particular  social 
concepts  of  a  given  time  impress  upon  all  economic  relationships 
on  account  of  which  they  appear  as  a  part  of  a  social  order,  all 
economic  relationships  are  taken  into  consideration  by  our  gen- 


eral  analysis  of  a  ''pure"  economic  system/-  The  further  realistic 
theory  must  therefore  consider  how  labor  is  handled  in  the  par- 
ticular economic  system  which  is  studied.  If  we  would  exhaust 
the  theory  of  location  of  industries  of  today,  if  we  would  explain 
fully  the  local  grouping  of  the  economic  forces  and  the  aggrega- 
tion of  population,  we  must  ask  what  it  means  for  the  local 
grouping  of  labor  that  labor  is  treated  as  a  commodity.  It  will 
be  seen  that  this  circumstance  determines  about  one-half  of  the 
local  distribution  of  our  present  social  system. 

"  The  interested  reader  may  with  profit  consult  Talcott  Parsons,  "  'Capital- 
ism' in  Recent  German  Literature:  Sombart  and  Weber,"  in  Journal  of  Politi- 
cal Economy,  vols.  XXXVI-VII,  and  the  Hterature  cited  there.  Cf.  also  above, 
page  10,  footnote,  on  the  concept  of  an  economic  system. — Editor. 


Georg  Pick 

Introductory  remark. — Upon  the  suggestion  of  the  author  of  this 
treatise  I  have  attempted  to  outline  in  popular  form  some  mathe- 
matical considerations  which  are  necessary  for  an  understanding  of  the 
problem  of  locations.  Regarding  sections  I  and  II,  I  should  like  to 
refer  to  a  recent  treatise  of  Scheffers^  which  gives  the  necessary  mathe- 
matical aid  for  the  solution  of  such  problems.  The  formula  of  agglom- 
eration which  forms  the  main  part  of  Section  III  is  stated  in  analogy 
to  similar  problems  in  different  fields  of  apphcation.  I  wish  that  further 
formulas,  particularly  locational  figures  with  more  than  three  points, 
might  be  developed.  But  they  stiU  present  some  real  difficulties.^ 


§  I.  The  locational  triangle. — In  the  accompanying  figure,  A^  repre- 
sents the  material  deposit,  A  2  the  fuel  deposit,  A^  the  place  of  con- 
sumption. Let  us  suppose  that  a^  tons  of  material  and  02  tons  of  fuel 
are  needed  to  produce  a^  tons  of  the  product  (we  shall  assume  a^ 
always  to  be  i).  If  the  place  of  production  is  located  in  P,  at  a  distance 
of  ri  miles  from  ^1,^2  miles  from  A 2  and  r^,  miles  from  A^,  then  ^3  ( =  i) 
tons  of  produce  apparently  require  226 

K  =  a^r^-{-  02^2 + a^^r^, 

ton-miles  of  costs  of  transportation. 

For  which  positions  of  P  are  these  costs  as  small  as  possible?  It  is 
obvious  at  once  that  as  long  as  P  is  situated  outside  of  the  locational 

^  As  Mr.  Bauer  suggests,  the  whole  case  corresponds  rather  strikingly  to  certain 
parts  of  electrostatics,  particularly  equipotential  surfaces.  Cf.  J.  H.  Jeans,  The 
Mathematical  Theory  of  Electricity  and  Magnetism,  pp.  54  £f. — Editor. 

^  G.  Scheffers,  Funktionen  der  Abstände  von  festen  Punkten  (1900). 

3  For  an  attempted,  though  unsuccessful,  solution  of  this  problem,  the  reader 
may  consult  Launhardt,  "Die  Bestimmung  des  zweckmässigsten  Standorts  einer 
gewerbUchen  Anlage."  I  have  given  a  resume  of  the  pertinent  passage  beneath, 
p.  238. — Editor. 




triangle  Ä1A2A3,  any  approach  of  P  to  the  side  of  the  triangle  next  to 
F  must  result  in  shortening  all  three  distances  r^,  ra,  r^  and  thus  in 
lowering  the  costs  of  transportation.  The  locus  of  the  minimum  point 
cannot,  therefore,  lie  exterior  to  the  triangle.  It  lies  either  interior  to 
the  triangle  or  upon  its  boundary.  We  shall  begin  with  treating  the 
first  of  these  two  possibilities. 

§  2.  The  minimum  point  in  the  interior  of  the  locational  triangle. 
Mechanical  model. — The  mathematical  analysis  of  the  necessary  condi- 
tions'* or  the  point  of  lowest  costs  of  transportation  shows  the  following 

Fig.  44 

results.  Let  us  imagine  a  variable  point  mass  at  P  which  is  pulled  with 
the  force  a^  toward  ^i,  aa  toward  A2,  and  a^  toward  A^.  The  position  of 
P  for  which  these  three  forces  are  in  equilibrium  is  the  locus  of  the  mini- 
mum point. 

This  suggests  that  we  might  demonstrate  the  position  of  Pq  (as 
we  may  call  the  point  of  least  cost  of  transportation)  by  a  mechanical 
model  with  an  automatic  device.  This  leads  us  to  an  old  apparatus 

4  The  necessary  conditions  of  this  case  may  be  stated  as  f oUows :  The  function 
of  the  locus  K  has  in  its  minimum  point  the  differential  quotient  zero  in  all  direc- 
tions : 




(for  each  direction  of  s).  This  formula  gives  us  two  equations  for  the  necessary 
condition  the  significance  of  which  is  set  forth  in  the  text  (cf.  Scheffers,  loc.  cit.). 



which  was  invented  by  Varignon  to  demonstrate  the  parallelogram  of 
forces.  Upon  the  edge  of  a  graduated  circular  disk  three  little  rollers 
with  horizontal  axes  may  be  affixed.  Over  each  roller  runs  a  thread. 
The  three  inner  ends  of  the  threads  are  coupled  together  at  some  point, 
the  outer  ends  hang  down  and  may  bear  little  weights.  In  order  to  227 
realize  a  given  case,  we  shall  first  place  the  rollers  so  that  they  form  the 
corners  of  the  locational  triangle.  For  this  we  can  use  the  scale  upon 
the  edge  of  the  circular  disk.  After  this  we  load  the  three  threads  with 
weights  proportional  to  the  transport  weights  öi,  «2,  Ö3  for  which  we 

Fig.  45 

may  substitute  the  same  units  of  a  small  weight,  e.g.,  dekagram.  The 
connecting  point  will  move  by  itself  to  the  position  of  the  minimum 

§  3.  Geometrical  construction  of  Pq.  The  weight  triangle. — Figure  46 
shows  the  forces  Ö1,  02,  «3,  acting  upon  Po  as  straight-line  segments 
whose  length  is  proportional  to  the  force.  According  to  the  theorem  of 
the  parallelogram  of  forces  each  of  these  straight-line  segments  if  laid 
out  from  Po  opposite  its  own  direction  will  constitute  the  diagonal  of 
the  parallelogram  formed  by  the  other  two  straight-line  segments  pro- 
vided a  state  of  equihbrium  exists.  If  one  lays  out  the  three  balanced 
forces  (straight-line  segments)  following  each  other  in  their  proper 
direction  and  length,  a  closed  triangle  (G1G2G3  of  the  figure)  results. 




The  angles  of  this  triangle  TiTzTs  are  the  supplements  of  the  three  angles 
ßißzßs  which  are  formed  in  Po  by  the  straight  lines  connecting  Pq  with 
the  corners  AjA2Ay  This  may  be  seen  by  a  glance  at  Figure  46.  The 
triangle  G1G2G3,  which  is  fully  determined  in  advance  by  its  sides 
01^2^3  shall  be  called  weight  triangle.  This  weight  triangle  gives  us  the 
angles  71T2T3,  and  therefore  ßißiß^.  In  order  to  find  the  point  Po 
we  shall  have  to  determine  that  position  of  P  from  which  the  lines 
connecting  P  with  y4i^2^3  form  these  particular  angles,  or,  as  one 
sometimes  says,  that  position  of  P  from  which  ^2^43  is  seen  subtending 
the  angle  ß^,  A^A^,  the  angle  JÖ2,  ^1^2,  the  angle  ßi. 

Fig.  46 

§  4.  Continuation.  The  three  circles  of  construction. — In  order  that 
the  angle  A^PoA^  have  the  given  size  ß^,  Po  must  he  (according  to 
the  theorem  about  angles  at  the  circumference  of  a  circle)  upon  a  cer- 
tain arc  which  stretches  from  A^  to  A2.  But  Po  must  also  He  upon  a 
corresponding  arc  ^2^3,  because  ^2^0^ 3  should  have  the  given  size 
jSi;  and  finally  Po  must  lie  upon  arc  AA^  because  ^3Po.4i  =  jÖ2.  Hence 
we  only  have  to  construct  these  arcs  (two  suffice),  in  order  to  get  Po 
as  their  point  of  intersection  (Fig.  47). 

In  order  to  construct  the  arc  through  ^1^2  we  have  to  apply  the 
angle  (/33  — 90°)  to  A^A^  at  A^  and  A2,  so  that  an  isosceles  triangle  re- 
sults, with  its  apex  at  C.  (Fig.  48.)  This  apex  C  is  the  center  of 
the  required   circle,  which  may  therefore  be  constructed  at  once. 



Indeed  it  is  A2CAi  =  iSo°  —  2  (183  — 90°)  =  360°  — 2^83,  and  consequently 
the  salient  angle  at  C  is  equal  to  2ß^,  as  was  required.^ 

§  5.  Approach  of  the  position  of  the  minimum  point  to  the  boundary 
or  to  a  corner  of  the  locational  triangle. — When  does  Po  lie  near  one  of 
the  sides  of  the  triangle,  for  example  ^1^2^  3?  It  is  apparent  that  the 
angle  AzPoA^,  i.e.,  jSi  will  be  almost  equal  180°,  and  that  71  will  be 
almost  equal  0°.  The  weight  triangle  has  therefore  one  very  small 
angle;  consequently  the  subtending  side  Ö1  will  be  very  small,  too,  while 

Fig.  47 

the  other  two  02,  Ö3,  will  be  nearly  equal.  If  öi  becomes  zero  (and 
02  =  03),  Po  lies  upon  ^2^3.  This  is  apparent  anyway;  for  Aj  has  dis- 
appeared; the  locational  triangle  has  shrunk  to  a  locational  Hne  (Fig. 


When  does  Po  lie  near  a  corner,  for  example  A^?  It  is  evident  that 
in  that  case  the  angle  ^2Po^3,  i.e.,  jSi,  will  be  almost  equal  to  A2AiA^, 
that  is,  almost  equal  to  the  angle  a^  of  the  locational  triangle,  while  ßi 
would  be  noticeably  larger  if  Po  were  located  more  in  the  center  of  the 
locational  triangle.  Similarly,  71,  the  supplement  of  ßi,  is  now  almost 
equal  to  the  supplement  of  ai  (the  exterior  angle  of  the  locational  tri- 

s  Instead  of  this  construction,  we  may  state  the  following  rule :  Erect  a  tri- 
angle similar  to  the  weight  triangle  upon  each  of  the  three  sides  of  the  locational 
triangle.  The  circles  described  around  these  triangles  are  those  required. 




angle  at  ^i)  which  would  usually  be  considerably  smaller.  Hence  as 
long  as  the  angles  of  the  weight  triangle  are  smaller  than  the  cor- 
responding exterior  angles  of  the  locational  triangle,  Po  will  He  within 
the  interior  of  the  latter;  but  if  one  of  the  angles  of  G1G2G3,  for  example 
7i,  is  equal  to  the  corresponding  exterior  angle  oi  A^AiA^,  in  this  case 
i8o°  — tti,  then  Po  is  located  at  the  corresponding  corner,  A^. 

§  6.  Position  of  Po  in  one  of  the  corners.  The  cases  without  a  weight 
triangle. — We  shall  imagine  now  that  the  weight  triangle  G1G2G3  is 


Fig.  49 

undergoing  changes,  and  see  what  changes  of  the  position  of  Po  result 
from  it.  02,^3,  shall  remain  unaltered,  while  öi  is  increasing  gradually 
which  causes  the  opposite  angle  71  to  increase  also.  We  have  just  seen 
that  Po  goes  to  the  corner  A^,  when  71  has  reached  the  size  i8o°  — aj. 
What  will  happen  if  a^  and  71  increase  further?  Apparently  Po  remains 
in  its  position  at  ^i.  For  if  the  share  of  a^  is  already  so  considerable 
that  the  transport  from  yli  to  Po  must  be  avoided  altogether  in  order 
to  achieve  a  minimum  of  costs,  it  will  be  that  much  more  necessary 
230  when  the  relative  value  of  öi  increases  further. 

When  the  value  of  Ö1  has  become  equal  to  02  plus  a^,  71  has  become 
equal  to  180°,  in  other  words  the  weight  triangle  has  shrunk  into  a  line 
(Fig.  50).  If  fli  increases  further,  so  that  ai>  02+^3,  no  triangle  can 


be  constructed  out  of  Ö1,  Ö2,  Ö3,  and  the  weight  triangle  has  ceased  to 
exist.  But  still,  Po  lies  at  Aj.^ 

The  model  described  in  §  2  shows  the  right  position  of  Po  for  these 
cases,  provided  that  care  is  taken  to  prevent  the  connecting  point  of 
the  three  threads  from  sliding  over  the  rollers. 

§  7.  Comprehensive  recapitulation.  Characteristics  of  the  dißerent 
cases. — We  may,  then,  distinguish  three  separate  possibiH ties  which  may 
be  characterized  as  follows :  First,  weight  triangle  exists,  Po  hes  in  the 
interior  of  the  locational  triangle;  second,  weight  triangle  exists,  Po 
lies  in  one  of  the  corners;  third,  weight  triangle  is  lacking,  Po  lies  al- 
ways in  one  corner.  But  while  the  third  case  can  be  recognized  at  once 

Fig.  50 

because  of  the  impossibihty  of  constructing  a  weight  triangle,  it  re- 
mains to  give  an  additional  characteristic  in  order  to  distinguish  the 
first  two  cases.  Let  us  recall  the  circles  of  construction  in  §  4.  As  long  as 
Po  lies  in  the  center  of  the  locational  triangle,  these  circles  intersect  in 
the  interior  of  the  triangle,  each  of  them  excluding  the  corresponding 
third  angle.  If  Po  approaches  the  corner  A^,  the  arc  over  ^2^3  passes 
near  Ai,  and  if  Po  reaches  A^  (because,  as  we  have  seen  in  §  5,  7i  = 
i8o°  — tti)  this  arc  passes  through  Ai  and  intersects  there  with  the 
other  two  circles.  If  71  increases  further,  the  arc  subtending  ^2^3  will  231 
go  beyond  ^i,  so  that  Aj  will  come  to  lie  in  its  interior.  The  point  of 
intersection  of  the  three  circles  now  falls  entirely  outside  of  the  loca- 
tional triangle.  At  the  same  time  this  point  ceases  to  be  a  solution  of 
our  problem;  for  Po  remains  at  ^i.  The  second  case  can  be  recognized 
by  the  fact  that  one  of  the  circles  of  construction  includes  the  third 
(i.e.,  that  corner  which  does  not  he  upon  its  base);  in  this  case  this 
included  corner  is  always  the  minimum  point. 

^  In  these  instances  where  Po  lies  in  one  of  the  corners,  other  conditions  prevail 
those  indicated  in  footnote  4.  - 
Po,  and  usually  not  equal  to  zero  at  Po. 

J  7^ 

than  those  indicated  in  footnote  4.  —  is  now  positive  in  all  directions  from 


§  8.  The  behavior  of  Pq  when  the  weights  ai,  Ö2,  ^3,  remain  unchanged, 
but  the  locational  triangle  changes. — We  have  investigated  the  changes 
of  the  position  of  Pq  which  are  caused  by  changing  the  transport 
weights  Ö1,  02,  öj  while  the  locational  triangle  remains  unchanged.  We 
shall  now  suppose  öi,  ^2,  %  fixed,  while  we  change  the  form  of  the  loca- 
tional triangle,  and  we  shall  observe  how  Pq  acts  under  these  condi- 
tions. Let  us,  moreover,  suppose  two  corners,  perhaps  A-,,  A2,  fixed; 
only  the  third  corner,  ^3,  shall  move. 

Let  us  first  take  up  those  cases  without  a  weight  triangle,  where 
one  of  the  three  weights  d,  aa,  ^3  exceeds  the  sum  of  the  other  two.  Ac- 

cording to  §  5,  Po  hes  at  A^  when  (Zi,  at  ^2  when  Ö2,  at  ^3  when  %  is 
the  large  weight.  Hence  Po  either  remains  unmovable  at  one  of  the 
fixed  corners  ^i,  A2,  or  Pq  participates  in  all  movements  of  A^,  always 
coinciding  with  this  point. 

§  9.  Continuation.  The  center  lies  upon  the  circle  through  Ai,  A2. — 
If  the  weight  triangle  exists,  we  can  take  from  it  the  angle  73  and  con- 
struct the  arc  over  A^Ai  as  was  shown  in  §  4  (Fig.  51).  It  is  necessary 
to  distinguish  whether  A^  Hes  in  the  segment  between  the  chord 
A1A2  and  the  arc  or  outside  of  it.  The  first  case  is  identical  with  the 
second  case  mentioned  in  §  7 :  Pq  coincides  with  A^  If,  however,  A^ 
lies  outside  of  the  segment,  then  the  construction  shown  in  §  4  takes 


place,  as  we  know  in  advance  that  Po  will  lie  upon  the  arc  A^Ai  itself. 
The  Hne  connecting  Po  with  ^3,  together  with  the  lines  connecting  Po 
with  ^i  and  .42,  forms  (cf.  §  3  and  §4)  the  angles  1 80°— 72  and  1 80°— 71. 
Its  extension  backward  beyond  Po  together  with  these  lines  includes 
the  fixed  angles  72,  7i.  Wherever  /I3  may  be,  Po  will  lie  upon  the  arc  232 
through  ^1^2,  in  such  a  way  that  the  extension  of  A^Po  together  with 
Po^i  always  includes  the  same  angle  71  at  the  point  Po.  According  to 
the  theorem  regarding  angles  at  the  circumference  of  a  circle,  PqA^ 
will  intersect  the  circle  through  A^,,  ^2  in  a  fixed  point  {M  of  Fig.  51) 
which  can  easily  be  constructed.  We  only  have  to  apply  the  angle  72 
at  A2  to  .42^3  downward,  and  the  second  side  of  this  angle  will  inter- 
sect the  circle  in  the  required  point  M. 

This  reasoning  is  correct  as  long  as  Po  does  not  coincide  with  one 
of  the  points  A-,,  A 2.  Because  in  these  cases  there  is  no  longer  any 
reason  why  A^,  Po,  and  M  should  lie  upon  one  straight  line.  Indeed, 
it  is  apparent  that  Po  Hes  alv/ays  and  only  at  ^i,  if  ^3  lies  somewhere 
in  the  angular  space  which  falls  between  the  extension  of  MAi  beyond 
yli  and  the  extension  of  A2A1  beyond  Ai.  The  situation  regarding  A2 
is  analogous. 

Let  us  imagine  ^3  approaching  AjA2  from  a  great  distance  along 
any  line  going  through  M.  If  the  straight  line  upon  which  A^  is  ap- 
proaching crosses  the  line  going  through  A1A2  outside  of  the  segment 
AiA2,  Po  lies  fixed  either  in  Aj,  or  in  A2.  But  if  it  crosses  between  Ai 
and  A2,  Po  lies  at  the  point  of  intersection  of  A^M  with  the  arc  as  long 
as  A^  has  not  reached  the  segment  of  the  circle  subtending  ^1^2.  But 
as  soon  as  ^3  enters  into  the  interior  of  this  segment,  the  point  Po  will  be 
taken  along  and  will  always  be  combined  with  A^. 

While  A^  changes  its  position  in  the  entire  half-plane  above  the 
straight  line  going  through  ^1^2,  Po  always  remains  confined  to  the 
interior  and  the  boundary  of  the  segment  of  the  circle  subtended  by  A1A2. 

§  10.  Survey  figure  showing  the  changes  of  transport  costs  when  the 
position  of  A^  changes. — One  and  the  same  position  of  Po  may  cor- 
respond to  very  different  positions  of  A^,  as  has  just  been  seen.  But 
total  costs  of  transportation  change  with  the  position  of  Ay  We  will  233 
get  a  good  view  of  this  situation  if  we  connect  by  a  curve  all  those 
positions  of  A^  which  show  equal  costs  of  transportation.  These  curves 
show  (Fig.  52)  a  very  different  shape  in  the  different  parts  of  the  half- 



plane  extending  above  the  straight  Hne  going  through  Ä1A2.  In  the 
before-mentioned  angular  spaces  at  Aj  and  A2  they  are  apparently  con- 
centric arcs  around  Ai  and  A  2  respectively.  In  the  main  space  lying 
between  these  two  we  have  to  distinguish  again  the  segment  from  the 
exterior.  Within  the  segments  we  get  elHptic  curves;  but  in  the  ex- 
terior one  curve  results  from  another  if  we  move  its  points  the  same 
distance  upon  each  of  the  straight  lines  through  M.  At  the  Hnes  sep- 
arating the  four  spaces  the  curves  appear  broken. 


^,  Curves  of  equal  transportation  costs,  when 
-r^"  one  deposit  is  movable.  If  A^  goes  from  one 
P      line  to  the  next,  the  transportation  costs  in- 

crease  to  the  extent  of  the  straight  line 

1^  11  10   9 

8     9    10  11  12 

Fig.  52 

§  II.  Two  locational  triangles  in  mutual  relation. — ^Two  locational 
triangles  A^AzA^  and  ^MMa  shall  be  related  in  such  a  way  that  A^ 
is  at  the  same  time  the  place  of  production  for  the  first  triangle  and  A^ 
at  the  same  time  the  place  of  production  for  the  second  triangle.  In  view 
of  this  quality  we  shall  designate  these  points  as  Po,  Po-  We  shall  as- 
sume the  locations  A1A2  and  ^3^2  and  the  two  sets  of  weights  a^,  02, 
«3  and  a'l,  a'2,  a'^  as  given.  The  points  required  are  Po  =  ^i  and  Po  =  ^3 
in  such  a  position  that  total  costs  of  transportation  become  as  smaU 
234  as  possible.  Those  cases  in  which  no  weight  triangle  exists  in  one  of 
the  two  locational  triangles  are  extreme  cases.  If  this  is,  for  example, 
the  case  with  regard  to  the  first  set  a^,  02,  Ö3,  then  Po=Ai  must  lie 
combined  either  with  Aj,  or  A2  or  with  A.=Fo.  We  therefore  either 



have  A'l  given  at  once,  or  the  two  places  of  production  are  combined, 
which  would  mean  that  one  place  of  production  for  four  given  points 
would  have  to  be  found.  Separate  places  of  production  located  else- 
where than  in  the  given  points  are  only  possible,  therefore,  if  both 
weight  triangles  exist.  Under  this  condition  the  two  segments  sub- 
tending AjAz  and  A'^Az  exist  as  has  been  discussed  in  §  9.  We  get  the 


\   /I 
\  / 1 

\     / 

'i  / 

\  / 


i'  / 


Fig.  53 

two  points  M  and  M'.  If  we  connect  therefore  M  with  M',  the  con- 
necting line  will  cut  the  two  circles  at  the  required  points  (Fig.  53). 

But  this  rule  is  subject  to  several  limitations.  If  the  segments  over- 
lap in  part,  and  MM'  traverses  the  common  part,  then  Po  and  P'o  are 
combined  (according  to  §  9)  and  may  not  lie  upon  MM'.  We  get  again 
the  case  of  one  place  of  production  with  four  determining  points.  If, 


on  the  other  hand,  MM'  does  not  meet  one  of  the  segments  at  all,  then 
■  Fo  or  P^  will  Ue  in  one  of  the  corners  A^,  A2  and  A'^,  A2  respectively 
(cf.  Fig.  52) ;  in  other  words,  either  P«  or  P^  are  given  at  once  and  the 
remaining  problem  reduces  itself  to  the  fundamental  problem.  The 
exceptions  are  therefore  of  a  more  simple  nature  than  the  regular  case 
for  which  construction  Figure  53  brings  the  solution. 
235  §  12.  Locational  polygons  with  more  than  three  corners. — In  spite  of 

the  fact  that  generally  speaking  the  essential  part  of  the  problem  and 
the  principles  of  its  treatment  are  unchanged  in  the  case  of  locational 
figures  with  more  than  three  corners,  it  is  impossible  to  give  equally 
simple  rules  for  construction  even  in  the  next  higher  case  of  the  quad- 
rangle. It  is' worth  noting  that  the  mechanical  model  functions  in  aU 
these  higher  cases  (if  properly  adapted).  For  if  we  let  weights  corre- 
sponding to  the  sets  of  transport  weights  pull  threads  at  the  corners 
of  any  locational  figure,  the  point  at  which  these  threads  are  coupled 
together  will  automatically  go  to  the  minimum  point. ^ 

7  Cf .  for  the  contrary  opinion,  Launhardt,  "Die  Bestimmung  des  zweckmässig- 
sten  Standorts  einer  gewerblichen  Anlage,"  in  Zeitschrift  des  Vereins  Deutscher  In- 
genieure (1882),  pp.  107,  iio-ii.  In  this  short  essa}-  Launhardt  is  concerned  mth 
figuring  out  the  most  favorable  location  of  an  isolated  process  of  production  which 
uses  only  localized  materials.  Although  this  is  a  very  narrow  and  limited  aspect  of 
the  problem  of  industrial  location,  it  seems  desirable  to  give  a  short  resume  of  his 
geometrical  arguments,  because  they  lead  him  to  the  conclusion  that  the  construc- 
tion of  minimum  points  is  possible  for  polygons  with  any  number  of  corners. 

After  having  arrived  at  the  conclusion  that  "the  kilometric  costs  of  transporta- 
tion must  hold  each  other  in  balance  at  the  location  of  production,"  he  finds  the 
minimum  point  by  constructing  a  triangle  similar  to  the  weight  triangle  upon  the 
side  A1A2  of  the  locational  triangle.  He  then  describes  the  circle  around  this  triangle 
and  connects  the  third  corner  O  of  this  triangle  with  the  third  corner  of  the  loca- 
tional triangle,  A^  (it  will  be  observed  that  this  involves  the  simpnf3dng  assumption 
that  A^  is  always  the  center  of  consumption,  while  the  reasoning  of  Pick  is  entirely 
independent  of  the  question  as  to  which  of  the  three  points  is  the  center  of  con- 
sumption) .  The  point  Po  at  which  this  connecting  fine  intersects  the  circumference 
of  the  circle  is  the  required  minimum  point.  Launhardt  calls  the  point  0  mentioned 
above  the  "pole"  of  the  locational  triangle. 

Using  the  theorem  of  Ptolemy,  Launhardt  proceeds  to  analyze  locational 
polygons  with  the  aid  of  his  construction  of  a  "pole"  (cf.  Fig.  53A).  He  thus  re- 
places both  Ai  and  A2.  This  substitution  of  the  pole  O  for  ^i  and  A2  becomes  the 
basis  of  his  construction  of  the  minimum  point  for  a  quadrangle,  Ax  A2  A^  A^/io. 
which  ^3  is  again  fixed  as  the  place  of  consumption.  What  he  does  is  simply  to 


Even  for  distinguishing  the  cases  where  the  minimum  point  P^  lies 
in  the  interior  from  those  cases  where  it  Hes  at  the  corners  of  the  loca- 
tional  figure,  we  do  not  have  those  simple  criteria  which  we  had  in  the 
case  of  the  triangle.  Suffice  it  to  indicate  that  Po  will  apparently  lie 
at  one  of  the  corners,  if  the  weight  of  that  corner  equals  or  exceeds  the 
sum  of  all  others  (Fig.  54). 

construct  a  "pole"  for  A2  and  A^,  and  then  construct  another  "pole"  for  Ai  and  0. 
The  line  connecting  this  second  pole  Q  with  A^  will,  Launhardt  believes,  give  the 
minimum  point  Po  where  it  intersects  the  circle  described  around  the  triangle  AiQO. 
Launhardt  does  not  attempt  to  prove  his  contention.  It  appears  to  be  wrong. 
Neglecting  the  (rather  important)  circumstance  that  it  is  not  apparent  just  on 


Fig.  53 a 

what  basis  these  two  poles  are  constructed  (inasmuch  as  in  the  fundamental 
case  of  a  triangle  they  were  found  by  constructing  a  triangle  similar  to  the  weight 
triangle  which  does  not  exist  here,  since  we  are  dealing  with  a  quadrangle),  the 
obvious  objection  to  it  is  that  it  involves  a  detour,  and  therefore  additional  costs 
of  transportation  for  the  materials  coming  from  A2  and  ^4  to  P.  It  is  difiicult  to  see 
how,  in  view  of  this  fact,  it  could  have  escaped  Launhardt's  attention  that  he  was 
not  reaUy  getting  a  minimum  point  at  aU.  Moreover,  he  himself  observed  that  a 
second  and  different  solution  is  possible.  This,  he  says,  is  achieved  by  constructing 
first  a  "pole"  O'  for  the  points  Ai  and  A^,  and  by  then  determining  the  location  Po 
for  the  remaining  points  A^,  A2  and  O'  through  their  "pole"  Q' .  Was  this  fact  in 
itself  not  an  indication  that  the  real  minimum  point  lay  somewhere  in  between 
these  two?  There  is,  as  a  matter  of  fact,  still  another  and  third  possibility,  namely 
to  begin  with  Ai  and  A2. 

It  is  surprising  that  Bortkiewicz,  in  his  review  of  Weber's  theory  {Archiv  für 
Sozialwissenschajt  und  Sozialpolitik,  19 10)  should  not  have  noted  these  fundamental 
limitations  and  errors  in  Launhardt's  essay  when  he,  at  the  same  time,  asserted 
that  Launhardt  had  done  before  what  Pick  is  setting  forth  in  this  Appendix. — 



§  I.  The  concept  oj  the  isodapanes. — If  in  any  locational  figures  the 
transport  weights  fl«  are  known  and  the  minimum  point  Po  ascertained 
and  still  the  place  of  production  is  not  located  at  Po,  then  costs  higher 
than  the  minimal  costs  will  be  incurred.  It  is  imaginable  that  the  place 
of  production  gradually  moves  away  from  Po  in  any  and  all  directions. 
In  every  direction  the  costs  of  transportation  will  rise  gradually  and 
may  reach  any  amount,  provided  only  we  move  the  place  of  produc- 
tion far  enough  away  from  Po.  Smaller  costs  of  transportation  than  in 

Fig.  54 

Po  of  course  cannot  be  found  anywhere;  but  it  is  obvious  that  we  shall 
be  able  to  find  loci  for  any  amount  of  transport  costs  higher  than  those 
238  in  Po,  and  we  will  be  able  to  find  such  loci  in  every  direction  from  Po. 
Consequently  there  exists  not  only  one  such  locus,  but  a  closed  curve 
around  Po  which  consists  of  all  the  loci  having  equal  costs  of  trans- 
portation. Such  a  curve  (curve  of  equal  transport  costs,  level  curve  of 
transport  costs,  isodapane)  will  exist  for  any  value  of  total  transporta- 
tion costs,  provided  only  that  such  value  is  higher  than  the  minimum. 
The  totality  of  these  curves  gives  a  clear  picture  of  the  way  in  which 
the  transport  costs  depend  upon  the  location  of  the  place  of  produc- 
tion. If  the  minimum  is  M  ton-miles,  we  may  draw  the  isodapane  for 
each  additional  10  ton-miles;  in  other  words,  those  curves  upon  which 
the  costs  of  transportation  would  be  M-{-io,  M-\-2o,  M+30,  etc., 
ton-miles  (cf.  Figs.  55-58). 

§  2.  Isodapanes  for  very  high  values  of  costs  are  approximately  circles. 
— Very  high  transport  costs  have  loci  which  are  very  far  away  from 
Po  and  the  locational  figure  too.  If  this  distance  is  so  considerable  that 



the  dimensions  of  the  polygon  appear  insignificant,  then  that  distance 
becomes  the  only  determining  factor.  Hence  those  curves  which  cor- 
respond to  very  large  costs  of  transportation  will  not  differ  very  con- 
siderably from  large  circles  around  Pq  as  center.  If  the  radius  of  such 

Fig.  55. — Isodapanes  I.  Ratio  of  weights:  3,  4,  5.  The  minimum  costs  of 
transportation  are  represented  by  Mo,  their  increment  from  one  isodapane  to  the 
next  by  m. 

a  circle  is  R,  the  transport  costs  for  some  location  of  the  place  of  pro- 
duction upon  its  circumference  are  approximately  equal  to 

i?(ai+Ö2+Ö3+Ö4  .  .  .  .)  ton-miles, 

because  it  is  admissible  to  assume  without  noticeable  error  that  all 
locations  are  united  in  Pq.  If  we  designate  the  sum 


that  is  the  total  weight  which  has  to  be  moved  for  the  production  and 
distribution  of  one  ton  of  product,  as  G  (locational  weight),  we  can 


Fig.  56. — Isodapanes  II.  Ratio  of  weights:  3,  4,  6 


Fig.  57.— Isodapanes  III.  Ratio  of  weights:  3,  4,  8 



formulate  the  following  rule:  The  transport  costs  for  places  of  pro- 
duction very  far  away  from  the  locational  figure  are  to  be  found  by 
multiplying  the  locational  weight  with  the  distance  of  the  place  of  pro- 
duction from  the  minimum  point:  GXR. 

If  the  isodapanes  are  drawn  for  a  certain  gradation  of  the  trans- 
portation costs,  as  indicated  in  i,  these  large  circles  will  he  the  closer 
the  larger  the  locational  weight  is.  For  the  larger  G  is,  the  smaller  is 

Fig.  58. — Isodapanes  IV.  Ratio  of  weights:  3,  4,  12 

the  increment  of  R  which  is  necessary  for  causing  the  same  increase  of 

§  3.  Smaller  values  of  the  transport  costs.  The  descent  of  the  transporta- 
tion costs. — If  we  pass  now  to  smaller  values  of  the  transport  costs,  the 
corresponding  isodapane  will  run  closer  round  the  locational  figure.  At 
the  same  time  the  shape  of  the  locational  figure  and  the  distribution 
of  the  sets  of  weights  Ö1,  ^2,  a^,  .  .  .  .  between  the  several  corners  will 
exert  an  increasing  influence  upon  the  shape  of  the  isodapane,  which 
wiU  differ  from  the  shape  of  a  circle  the  more,  the  less  the  transport 
costs  exceed  the  minimum,  i.e.,  the  closer  the  isodapane  runs  round 
Fo.  Under  all  circumstances  the  system  of  curves  which  we  have  drawn 
will  show  us  the  following:  If  we  transfer  the  place  of  production  from 
one  isodapane  to  the  one  next  farther  away  from  Po,  we  shall  increase 



the  transport  costs  by  lo  ton-miles.  It  follows  that  if  we  leave  an 
isodapane  in  the  perpendicular  direction  away  from  Po,  the  transport 
costs  increase,  and  they  do  so  the  faster  the  nearer  the  next  isodapane 
is  to  the  one  left.  If,  for  example,  the  distance  from  the  next  isodapane 
is  5  miles,  these  5  miles  cause  an  increment  to  the  transport  costs  of 
10  ton-miles;  if  the  distance  had  been  10  miles,  we  would  get  the  same 
increment  of  costs  only  after  10  miles.  In  the  first  instance  the  addi- 
tional costs  for  I  mile  are  2  ton-miles.  If  we  caU  the  amount  by  which 
the  transport  costs  are  increased  when  the  place  of  production  is  moved 
away  from  Po  i  mile  in  a  perpendicular  direction,  the  descent  of  the 
transport  costs,  we  can  derive  the  following  rule  for  the  determination 
of  this  value:  Divide  ten  by  the  distance  of  adjoining  isodapanes.* 
The  closer  the  isodapanes  follow  each  other,  the  larger  is  this  descent. 

§  4.  Illustration  by  a  spatial  model.  {Surface  of  transport  costs.) — Let 
us  imagine  that  we  had  raised  a  perpendicular  straight  line  at  each 
possible  position  of  P  in  the  plane,  giving  this  perpendicular  line  the 
length  corresponding  to  the  sum  of  transport  costs  at  the  point  where 
it  is  raised.  In  this  way  we  shall  get  above  each  position  of  P  a  point 
240  in  space,  and  all  these  points  together  constitute  a  surface.  The  lowest 
point  of  this  surface  lies  above  the  point  Po;  right  around  it  the  surface 
rises,  and  at  a  certain  distance  from  P«  it  does  not  differ  very  noticeably 
any  longer  from  a  conical  surface  whose  vertical  axis  goes  through  Po, 
although  it  shows  an  irregular  shape  around  the  lowest  point.  If  we 
go  along  upon  this  surface  in  such  fashion  that  the  distance  above  the 
ground  plain  remains  unaltered,  we  shall  be  moving  along  an  isoda- 
pane. The  steepest  ascent  at  any  particular  point  is  given  by  the  line 
which  runs  perpendicular  to  this  isodapane.  The  steeper  the  ascent  is, 
the  faster  do  the  costs  of  transportation  increase  if  we  move  away 
from  the  isodapane  in  a  perpendicular  direction.  The  steepness  gives 
an  immediate  picture  of  the  descent  of  the  transport  costs. 

5.  The  picture  of  the  system  of  isodapanes  in  the  immediate  neigh- 
borhood of  Po. — In  the  immediate  neighborhood  of  Po  the  distribution 
of  the  isodapanes,  and  in  connection  therewith  the  shape  of  the  surfaces 
of  transport  costs,  differ  widely,  in  accordance  with  the  main  cases 

8  Such  inexact  explanation  of  this  concept  may  suffice  here.  In  truth  what  is 
involved  is  the  differential  quotient  (taken  with  the  inverse  sign)  -^  of  the  trans- 
port costs  in  that  direction  in  which  K  decreases  fastest. 


given  in  I,  §  7.  If  Po  lies  in  the  interior  of  the  locational  figure,  the  first 
isodapane  following  Po  (given  fixed  gradation,  e.g.,  the  10  ton-mile 
increment)  will  be  fairly  far  away  from  Po  on  all  sides,  due  to  the  fact 
that  strictly  speaking  the  descent  has  the  value  zero  in  Po.  The  same 
is  true  when  Po  is  located  in  one  of  the  corners,  as  long  at  least  as  the 
corresponding  weight  does  not  exceed  the  sum  of  the  others  consider- 
ably. But  it  appears  at  once  that  the  first  isodapane,  in  so  far  as  it  runs 
outside  of  the  locational  figure,  runs  much  closer  to  Po  than  it  does  in 
the  interior.  But  if  the  weight  attached  to  the  particular  corner  be- 
comes very  considerable,  the  first  isodapane  approaches  the  point  Po 
correspondingly  from  all  sides,  so  that  it  surrounds  it  closer  as  the 

M\ \m 

Fig.  59 

weight  of  that  comer  increases  as  compared  with  the  sum  of  the  others. 
The  surfaces  of  transport  costs  will  in  the  first  case  have  the  shape  of  a 
very  shallow  depression  which  in  the  case  of  location  in  the  corner  wiU 
be  somewhat  steeper  outside  than  inside  of  the  figure.  In  the  case  of 
considerable  weight  at  one  corner,  however,  the  surfaces  will  exhibit 
a  more  or  less  steeply  funnel-shaped  depression.  The  Figures  55-58 
will  give  a  clear  idea  of  all  these  aspects,  since  they  correspond  to  our 
different  assumptions. 


§  I.  The  function  of  economy  and  its  diagram. — A  large  unit  of  pro-  241 
duction  having  the  daily  quantum  of  production  M  wiU  absorb  (ag- 
glomerate) a  small  unit  of  production  of  the  same  kind  having  the 
daily  quantum  of  production  m  and  lying  at  the  distance  r,  if  the  econ- 
omies resulting  from  the  agglomeration  are  greater  than  the  resulting 
increase  of  costs  of  transportation.  The  latter  is  easy  to  calculate.  If 
A  is  the  locational  weight  of  production,  the  additional  costs  for  one 
ton  of  product  apparently  amount  to  ^r  ton-miles.  The  total  addi- 
tional cost  amounts  to  Arm  ton-miles,  or  Arms  money-units,  if  5  is 
the  transport  rate. 

The  economies  which  result  from  agglomeration  depend  upon  the 
kind  of  production.  For  each  species  we  may  imagine  that  we  had  set 
down  in  a  tabular  form  the  economies  per  ton  of  daily  product  which 



occur  for  each  and  any  amount  of  agglomeration.  Such  economies  are 
caused  by  the  quantum  of  agglomeration  M;  they  are  a  function  of  M. 
We  shall  call  it  the  function  of  economy  0  {M).  Instead  of  giving  it  in 
the  form  of  a  table,  as  just  mentioned,  we  may  present  it  very  clearly 
by  a  geometrical  figure.  Let  us  lay  out  the  values  M  from  the  point 
of  intersection  of  two  axes  perpendicular  to  each  other.  These  straight 
line  segments  M  are  called  abscissae.  Then  we  raise  a  perpendicular  at 
the  extreme  point  of  each  abscissa  and  give  it  the  length  of  the  cor- 
responding function  of  economy  0  {M).  These  lines  are  called  ordi- 
nates.   By  this  operation  we  get  points  in  the  plane  which  together 

Fig.  60 


constitute  a  curve,  which  presents  the  total  course  of  the  function  of 

§2.  The  basic  formula  of  agglomeration.  The  function  of  agglomera- 
tion.— If  M  is  the  quantum  of  a  large  unit  of  production,  the  economies 
produced  by  agglomeration  will  be  0  (M)  for  each  unit  of  product,  and 

M  <j>{M) 

for  the  daily  product. 

If  the  small  unit  of  production  having  the  quantum  of  production 
m  is  combined  with  the  larger  unit,  we  shall  get  total  economies 
amounting  to 

{M-{-m)4){M-\-m) . 


Accordingly  the  increase  of  economies  due  to  agglomeration  is 
(M+ w)(/)(M+w)  -M<t>{M)  . 

As  long  as  this  value  is  larger  than  the  increase  in  costs  of  transporta- 
tion, Arsm  (cf.  above),  the  agglomeration  will  actually  take  place.  We 
get  therefore  the  following  equation  for  calculating  the  largest  distance 
R  to  which  the  absorbing  force  of  the  large  unit  of  production  extends: 

ARs  = 



The  right  side  of  this  equation  contains  M  as  well  as  m.  If  m  were  at  all 
considerable,  it  would  indeed  have  an  influence  upon  the  magnitude 


Fig.  61 

of  R.  But  the  nature  of  the  problem  under  discussion  involves  that  m 
is  a  very  small  quantity  as  compared  with  M.  In  view  of  that  the  right 
side  of  the  equation  becomes  quite  independent  of  m,  it  becomes  a 
function  of  M  alone;  but  let  us  imagine  for  once  that  the  equation  con- 
tains first  the  value  m  and  then  twice  the  value  2m.  In  Figure  61  we 
see  three  rectangles  incasing  each  other.  Their  area  apparently  is 

M<f)(M),  (M+m)<t>{M+m),  (M+2m)4>{M-\-2m)  , 

respectively.  Their  differences,  figures  of  a  kind  which  the  ancients 
called  gnomon,  are  decisive  for  the  previously  given  quantities.  The 

big  gnomon 



apparently  approaches  being  twice  as  large  as  its  part 

{M-^m)<i>{M-\-m)-M(j>{M) , 

243  as  m  decreases.  This  gives  us 

(M+  2m)(t){M+  2m)-M4>{M)  ^  {M-\-m)4>{M-\-m)  -M(t)(M) 
2m  m  ' 

and  this  equation  is  the  basis  of  the  independence  which  we  have 

The  function 

.^.  ^  {M^m)4>{M^m)-Mcf>{M) 

shall  be  called  the  function  of  agglomeration.  Our  previous  formula 
is  now  transformed  into 


and  this  is  the  basic  formula  of  agglomeration.  It  shows  that  the 
radius  within  which  the  agglomerating  force  of  a  production  of  the 
quantum  M  is  effective,  is  directly  proportional  to  the  value  of  the 
function  of  agglomeration,  while  it  is  inversely  proportional  to  the 
locational  weight  and  the  transport  rate. 

§  3.  Diagram  of  the  function  of  agglomeration. — In  order  to  get  a 
clear  survey,  we  shall  imagine  now  that  the  function  of  agglomeration, 
as  the  function  of  economy  before,  is  presented  in  a  diagram  (Fig.  62). 
In  this  diagram  the  perpendiculars  upon  the  axis  raised  at  the  extreme 
points  of  the  several  M  have  the  length /(JW).  Above  a  small  segment 
having  the  length  m  which  has  been  laid  out  from  the  extreme  point 
of  M,  there  lies  a  strip  of  plane.  This  plane  is  bounded  on  both  sides 
by  the  ordinates/  (M)  and/Cilf+w)  and  on  top  by  the  curve  of  our 
diagram.  We  will  be  able  to  calculate  this  strip  as  a  rectangle  ha\dng 
the  base  m  and  the  altitude  f{M)  the  more  accurately  the  smaller  m 
is.  This  strip  had  the  area 

244  mf(M)  =  {M-\-m)<l){M+m)-M4>{M) , 

and  thus  represents  the  increment  of  daily  economies  which  results 
when  agglomeration  progresses  from  the  values  M  to  the  value  M-\-m. 



If  we  now  look  at  the  entire  plane  above  the  abscissa  M  which  is 
bounded  by  the  curve  of  the  diagram  and  the  ordinates,  we  can  see 
that  it  is  possible  to  conceive  it  as  being  divided  into  a  whole  series 
of  strips.  The  value  of  this  plane  is,  therefore,  nothing  but  the  sum 
of  all  the  increments  of  economies  from  the  beginning  of  the  process  of 
agglomeration  up  to  the  altitude  M;  in  other  words,  the  total  econ- 
omies of  agglomeration  at  M.  It  equals 

Mc}>{M)  . 

Finally  we  may  even  get  an  idea  of  (f){M)  itself.  Let  us  imagine  (Fig. 
62)  the  two  axes  and  the  ordinate  of  M  being  impermeable  walls  and 

f — 

1      1    ' 

1    1  1 
1    1  ' 


'.I   \  .u 


M  M+m 

Fig.  62 

the  plane  just  mentioned  as  consisting  of  inflexible  metal  bounded 
in  front  and  in  back  by  parallel  plates.  If  the  metal  would  be  liquefied 
now,  it  will  readjust  itseK  so  as  to  have  a  horizontal  surface.  Since  the 
area  of  the  resulting  rectangular  figure  is  M0(M),  and  its  base  is  M, 
the  altitude  gives  us  4){M).^ 

9  Higher  mathematics  will  express  the  relations  which  we  have  discussed  and 
which  exist  between  the  function  of  economy  and  that  of  agglomeration  by  saying: 
The  function  of  agglomeration  is  the  differential  quotient  of  the  function  of  economy 
multiplied  by  M: 





§  4.  Agglomeration  of  small  units  of  production  which  have  been  uni- 
formly distributed. — Let  us  imagine  small  units  of  production  which  are 
distributed  uniformly  throughout  a  certain  area.  If  a  large  unit  of  pro- 
duction develops  within  this  area  it  will  absorb  the  existing  smaller 
units  within  a  certain  radius.    If  we  wish  to  calcu- 
late  the  radius  with  the  help  of  our  formula  of 
agglomeration,  we  must  keep  in  mind  that  M  itself 
changes  and  increases  under  the  influence  of  the 
process  of  agglomeration.    We  designate  as  p  the 
amount  of  daily  production  which  is  produced  per 
jTjQ  53  unit  of  area  under  the  original  uniform  distribution. 

245  This  we  shall  call  density  of  production.    If  then 

(Fig.  63)  a  large  unit  of  production  at  G  has  absorbed  all  production 
just  up  to  the  circumference  of  the  circle  with  the  radius  R,  it  must 
have  reached  the  quantity 

ttR'  p. 

Therefore  this  value  for  M  must  be  introduced  into  the  formula  of 
agglomeration,  or  R  must  be  calculated  from 

ttR^  P=M  : 

and  then  introduced.  We  thus  get 

ARs=f{TrR'p)  , 

or  respectively 




From  this  equation  we  shall  have  to  calculate  M.  This  is  of  course 
possible  only  if  the  function  of  agglomeration  f{M)  is  known.  But  if 
we  have  found  the  value  of  M,  the  quantum  of  agglomeration,  then  it 
is  easy  to  give  the  approximate  number  of  large  units  of  production 
which  have  come  into  existence  in  the  area  dealt  with.  For  if  ß  indi- 
cates the  amount  of  daily  production  in  the  entire  area,  the  number  will 

apparently  be 





§  5.  Ascertaining  the  quantum  of  agglomeration  through  the  diagram 
of  the  function  of  agglomeration. — According  to  what  has  been  said  the 
problem  is  now  to  determine  M  in  such  a  way  that 


VM=f(M)  . 


We  shall  imagine  that  we  had  laid  out  a  second  curve  in  the  figure 

which  contains  the  graphic  presentation  of  f{M)  by  co-ordinating  to 

each  abscissa  M  the  ordinate 




(Fig.   64).    The  points  which  we  get  compose  a  well-known  curve, 
called  parabola.    The  required  abscissa  is  that  abscissa  for  which  the 


Fig.  64'° 

curve  off(M)  and  the  parabola  have  equal  ordinales;  in  other  words,  where 
both  curves  meet. 

There  exist  several  possibilities.  The  curve  oif(M)  may  right  from 
the  beginning  extend  beneath  the  parabola  and  remain  beneath  it.  In   246 
that  case  the  equation  is  never  fulfilled  and  always 

N}f(M) , 

'°  For  brevity's  sake  the  designation  2p= is  used  for  the  so-called  param- 


eter  {2p)  of  the  parabola. 


which  means  obviously  that  the  increments  of  transport  costs  are 
never  reached  by  the  economies  of  agglomeration  for  any  quantum  of 
agglomeration.  In  this  case  agglomeration  is  impossible. 

Second,  the  curve  of  f{M)  may  in  the  beginning  run  above  the 
parabola  and  then  cross  it  at  some  place  remaining  beneath  it  after 
that.  In  this  case  agglomeration  will  occur  up  to  that  quantum  which 
is  indicated  by  the  abscissa  of  the  point  of  intersection  of  the  two 

The  third  case  in  which  f{M)  runs  from  the  beginning  and  always 
above  the  parabola  does  not,  it  seems,  correspond  to  any  actual  cases. 


Agglomeration,  xxi,  xxvf.,  xxvii,  20  ff., 
24,  35;  Alfred  Weber's  theory  of,  124- 
72;  analysis  of  agglomerative  and 
deglomerative  factors,  124-34;  causes 
of,  3,  6;  definitions,  126  f.  Mathemati- 
cal considerations  of,  245-51;  and 
stages  of  production,  186  f.  See  also 
Laws  of  agglomeration;  Realities,  re- 
introducing the 

Agricultural  basis  of  industry,  37  f. 

Agricultural  production,  theory  of,  xiv, 
xviii,  XLX,  XX,  xxLx  f.,  5  ff. 

Assumptions,  Weber's  simplification  of, 
37-40;  the  assumption  of  a  separate 
basis  of  material  supply,  consump- 
tion, and  labor,  37  ff.;  the  considera- 
tion of  the  "forces  of  nature,"  39  f. 

Automobile  transport,  its  effect  upon 
location,  86  n. 

Bauer,  Paul  S.,  viii,  227  n. 
Böhm-Bawerk,  E.,  27  n. 
Bücher,  Karl,  10  n.,  190  n. 

Capital.  See  Fixed  capital 

Capitalistic  economic  order,  26 

Chamberlin,  E.  H.,  vii 

Chapin,  F.  Stuart,  14 

Clark,  A.  B.,  xxviii  n. 

Clark,  J.  M.,  xvii,  xxvii,  46  n. 

Coefficient  of  manufacture,  162-66 

Competition:  of  price,  19;  of  quality, 
18  f. 

Cost:  elements  of,  28  ff.  See  also  Labor 
cost,  Production  cost.  Transportation 
cost  of  production  and  labor  cost,  xii 

Cultural  factors  and  orientation  of  in- 
dustry, 21  f. 

Daggett,  Stuart  R.,  xxviii 

Deglomerative  factors  and  orientation 
of  industry,  xxi,  xxvf.,  20  ff.,  24, 
131  ff.  See  also  Agglomeration 

Distribution,  process  of,  4,  5,  25  ff.;  con- 
sumptive, 4;  productive,  4 

Distributive  process,  18  ff. 

Economic  system  or  order.  See  System 

Economy,  function  of,  162  ff. 

Elliot,  WüUam  Y.,  vii 

Engländer,  Oskar,  xxii  n.,  xxvii  n., 
xxviii  n.,  51  n. 

Enviromnent,  14;  and  labor  orientation, 

Equilibrium:  in  constructing  minimum 
point,  229;  of  location,  213;  in  Mar- 
shall, xiv 

Fixed  capital,  25  ff.,  30 
Formkoeffizient  ("the  coefficient  of  manu- 
facture"), 162-66 
Free  trade,  doctrine  of,  xxviii  ff , 

"General  expenses,"  28 

General  factors  of  location.  See  Loca- 

tional  factors 
Geographical  factors  and  orientation  of 

industry,  i,  21  f.,  24 

Haig,  R.  M.,  17  n. 

Halbfabrikat,  174.  See  also  Product 
HaU,  F.  S.,  xvii 
Haurath,  John  J.,  172  n. 
Hoover,  Herbert,  xi  n. 

Index  of  labor  costs,  106-8.  See  also 
Labor  index 

Index  of  manufacture,  164  ff. 

Insurance.  See  General  expenses 

International  distribution  of  industrial 
location,  15 

International  tariffs  and  theory  of  loca- 
tion, xxvii  f . 

International  theory  of  labor,  xxviii 

Isodapanes,  102-4,  122,  144  ff. 

Jeans,  J.  H.,  227  n. 

Krzyzanowski,  Wytold,  xvii  n. 

Labor  cost,  xxiff.,  20,  21,  27,  28,  33; 
analysis  of,  Weber's  theory  of,  95- 




loi;  and  cost  of  production,  John 
Stuart  Mill's  consideration  of,  xii; 
and  rent,  Thiinen's  theory  of,  xix 

Labor  index,  xxii.  See  also  Index  of 
labor  costs 

Labor  organization,  development  of, 
129  f. 

Labor  orientation,  95-123;  agglomera- 
tion and,  156-62;  and  the  stages  of 
production,  184-86.  See  also  Labor 
costs,  analysis  of;  Laws  of  labor 

Land  rent.  See  Rent;  also  Theory  of 

Lardner,  xvi  n. 

Launhardt,  227  n.,  238  n. 

Laws  of  labor  orientation,  102-23;  char- 
acter of  the  industries  and  labor  orien- 
tation, 107-17;  conditions  of  labor 
orientation,  105-7;  environmental 
conditions  of  labor  orientation,  117- 
20;  isodapanes,  102-4;  orientation  of 
an  entire  industry,  11 2-1 7;  orienta- 
tion of  an  individual  plant,  107-12; 
tendencies  of  development,  120-23; 
theoretical  solution,  102-4 

Laws  of  agglomeration,  134-62;  ag- 
glomeration in  the  case  of  an  increas- 
ing index,  143-47;  agglomeration  with 
fixed  index,  135-43;  agglomeration 
and  labor  orientation,  156-62;  ag- 
glomeration within  transport  orienta- 
tion, 135-56;  conditions  of  agglomera- 
tion, 147-53;  formula  of  agglomera- 
tion, 153-56 
Laws  of  industrial  location,  10 
Laws  of  transport  orientation,  48-75; 
cases,  61-67;  factors  of  the  transport- 
orientation,  7  2-73 ;  location  figures  and 
kinds  of  industrial  materials,  48-53; 
material  index,  locational  weight,  and 
theoretical  conclusion,  59-61;  mathe- 
matical solution,  53-59;  orientation  of 
an  entire  industry,  67-72;  tendencies 
of  development,  73-75 

List,  Friedrich,  xxix 

Location,  theory  of,  in  relation  to  theory 
of  land  rent,  xi-xxxi 

Locational  factors  and  locational  dy- 
namics, 17-36;  agglomerative  factors, 
20  ff.,  24;  ascertaining  the  general  fac- 
tors of  location,  21-34;  classification 

of  locational  factors,  20-23;  deglomer- 
ative  factors,  20  ff.,  24;  explanation  of 
terms,  17-20;  general  factors,  24; 
"locational  factor,"  definition  of,  18; 
"locational  unit,"  definition  of,  18  f.; 
regional  factors,  20  ff.,  240.,  34;  spe- 
cial factors  20;  theory  of  the  locational 
factors,  34-36 

Locational  figures.  See  Laws  of  trans- 
port orientation 

Locational  unit.  See  Locational  factors 

Locational  weight,  xxii,  108-12,  150  f., 
155  f.,  162  ff.  See  also  Laws  of  trans- 
port orientation 

Locus  of  least  cost  of  transportation, 

Manufacturing  industry  in  the  total 
economic  system,  211-26;  historical 
distribution  of  locations,  213  ff.;  the 
result  and  the  remaining  problem, 
221  ff;  the  strata  of  locational  dis- 
tribution and  their  interaction,  214  ff. 

Marketing  factors,  130  f.,  206-9 

Marshall,  Alfred,  xiii  ff ;  xxix 

Marshall,  Leon  C,  vii,  viii 

Mason,  Edward,  vii 

Material  index,  xxii.  See  also  Laws  of 
transport  orientation 

Materials:  cost  of,  xxi,  25  f.,  28,  32  f.; 
kinds  of  industrial,  48-53;  and  pro- 
ductive processes,  201-6 

Mathematical  Appendix  (by  Georg 
Pick),  227-52;  agglomeration,  245-51; 
lines  of  equal  transportation  costs, 
240-45;  the  locus  of  least  cost  of 
transportation,  227-39 

Mathematical  solution.  See  Laws  of 
transport  orientation 

Mill,  John  Stuart,  xi-xiv 

Minimum  costs.  See  Points  of  minimum 

Minimum  point.  See  Points  of  minimum 

Monopoly  and  theory  of  location,  xxvii 

National  disposition,  14 
Natural  factors  and  orientation  of  indus- 
try, xxix,  21  ff. 

Ohlin,  Bertil,  xxviii  n. 
Orientation.  See  Total  orientation 



Parsons,  Talcott,  vii,  226  n. 

Pick,  Georg,  viii,  227  ff. 

Pigou,  A.  C,  xi,  xxvii,  42  n. 

Points  of  minimum  costs  of  transporta- 
tion, 53  ff. ;  when  location  is  split, 

Political  interferences,  14 

Power,  cost  of,  xxi,  25  f.,  28,  32  f.;  use 
of  water  power,  89-94 

Predöhl,  Andreas,  vii,  xxiv,  xxvii  n., 
163  n.,  172  n. 

Price,  elements  of,  26  ff. 

Price  differences  of  materials  and  their 
effect,  88-89 

Price  levels  of  deposits  of  materials,  34 

Product :  half-finished,  1 74  f . 

Productive  advantage,  18  ff. 

Productive  process,  18  ff.;  and  distribu- 
tion process,  25  ff.;  interaction  of  the 
independent,  196-21 1;  organization  of 
the  stages  of  a  given,  174-96 

Produktionsstufengliederung,  173,  See 
also  Stages  of  production 

Profits,  28 

Raw  materials,  location  of,  xii,  xxi,  xxxi, 
19,  20,  32  f. 

Real  estate,  25  ff.,  31  f. 

"Realistic"  theory,  12  f. 

Realities  (agglomeration),  reintroducing 
the,  162-72;  coefficients  of  (value  add- 
ed through)  manufacture  (Form- 
koeßzient),  162-66;  forms  of  ag- 
glomeration in  reality,  166-67;  tend- 
encies of  development,  168-72 

Realities  (total  orientation),  reintroduc- 
ing the,  187-96 

Reality  (transport  orientation),  approxi- 
mations to,  76-94;  different  kinds  of 
transportation  systems  working  to- 
gether, 82-87;  a  divided  transporta- 
tion system,  81-82;  existing  system  of 
transportation  rates,  76-81;  further 
application  of  theory  to  reality,  88-94; 
price  differences  of  materials  and 
their  effect,  88-89;  real  nature  of  the 
transportation  system,  84-87;  use  of 
water  power,  89-94 

Regional  factors  and  orientation  of  in- 
dustries, xxi,  20  ff.,  24  ff.,  34,  124 

Rent:  cost  of,  20,  21;  land  rent,  theory 

of  location  in  relation  to  theory  of, 
xi-xxxi;  Marshall's  theory  of,  xivff.; 
Mill's  analysis  of,  in  its  relation  to 
value,  xiii;  Thiinen's  theory  of,  xLx. 
See  also  Real  estate 

Ricardo,  xii,  xiv,  xvii 

Ritschl,  Hans,  xxx  n.,  172  n,,  214  n. 

Roscher,  W.,  xvii,  6 

Ross,  Edward  A.,  xvii 

Salin,  Edgar,  xiv  n.,  xvii  n.,  172  n. 

Sax,  Emil,  41  n.,  46  n. 

Schaeffle,  Albert  E.  F.,  6 

Scheffers,  G.,  227  n. 

Schlier,  Otto,  171  n. 

Schumpeter,  Joseph,  xi  n. 

Shipping  costs.  See  Transportation  costs 

"Situation  rent,"  xv 

Smith,  Adam,  xi,  n.  5,  xiv 

Social  factors  and  orientation  of  indus- 
try, 21  ff. 

Sombart,  Werner,  xxiii,  38  n.,  225,  226  n. 
Sorokin,  P.,  14 
Sprachgeist,  vii 

"Stages"  of  production  and  transport 
orientation,  1 74  ff . 

"Stock"  of  industrial  workers,  14 
System,  the  economic:  its  relation  to 
labor  orientation,  225;  its  relation  to 
the  location  of  industry,  211  ff.;  its 
relation  to  locational  factors,  26;  as  a 
theoretical  concept,  10  n. 

Taussig,  Frank  W.,  vii,  42  n.,  43  n.,  46  n. 

Taxes.  See  General  expenses 

Technical  equipment,  development  of, 
128  f. 

Technical  factors  and  orientation  of  in- 
dustry, 21  ff. 

Theory,  economic,  i ;  its  relation  to  basic 
assumptions  in  theory  of  location, 
211  n.;  its  relation  to  the  concept  of  a 
"pure"  system  of  economics,  ion.,  225 

Theory  of  location:  importance  of  an 
economic  theory,  i;  limitation  to  a 
theory  of  the  location  of  manufactur- 
ing industry,  and  reasons  therefor,  3; 
methods  employed,  6;  results,  limita- 
tions of,  12  ff.,  212  ff. 



Theory  of  location  in  relation  to  theory 
of  land  rent,  xi-xxxi;  in  Alfred  Mar- 
shall, xiii-xxx;  in  John  Stuart  Mill, 
xi-xiv;  in  J.  H.  von  Thiinen,  xiii, 
xviii-xxiii,  xxvi,  xxvii,  xxix,  2,  5; 
in  Alfred  Weber,  vii,  viii,  xi,  xvi, 
xviii,  xx-xxx;  significance  for  a  theory 
of  monopoly  transportation  rates  and 
international  trade,  xxx 

Theory  of  the  locational  factors,  34-36 

Thiinen,  J.  H.  von,  xiii,  xviii-xxiii, 
xxvi,  xxvii,  xxix,  2,  5,  31  n,,  38  n., 
215  n.,  220,  223 

Total  orientation,  the,  173-210;  inter- 
action of  the  independent  productive 
processes,  196-210;  organization  of 
the  stages  of  a  given  productive 
process,  174-96 

Transport  orientation,  41-94;  agglomer- 
ation within,  135-56;  and  the  stages 
of  production,  173-83.  See  also  Laws 
of  transport  orientation;  Reality,  ap- 

proximations     to;       Transportation 
costs,  analysis  of 

Transportation  costs,  xii,  xviii,  xxiff., 
20,  21,  27  f.,  33,  34  f.,  150;  analysis  of, 
41-48;  locus  of  least  cost,  227-39 

Transportation  rates  and  theory  of  loca- 
tion, xxvii  f .  See  also  Transportation 
cost;  Reality,  approximations  to 

Transportorientierung.  See  Transport 

Value,  John  Stuart  Mill's  consideration 
of,  xii  ff . 

Wages.  See  Labor  cost 

Water  power,  use  of,  89-94 

Water  supply,  20 

Weber,  Alfred,  vii,  viii,  xi,  xvi,  xviii, 

Wissler,  Clark,  14  n. 

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